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Abundant rogue wave solutions for the (2 + 1)-dimensional generalized Korteweg–de Vries equation Int. J. Nonlinear Sci. Numer. Simul. (IF 1.467) Pub Date : 2020-12-21 Huanhuan Lu; Yufeng Zhang
In this paper, we analyse two types of rogue wave solutions generated from two improved ansatzs, to the (2 + 1)-dimensional generalized Korteweg–de Vries equation. With symbolic computation, the first-order rogue waves, second-order rogue waves, third-order rogue waves are generated directly from the first ansatz. Based on the Hirota bilinear formulation, another type of one-rogue waves and two-rogue
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Anthropogenic climate change on a non-linear arctic sea-ice model of fractional Duffing oscillator Int. J. Nonlinear Sci. Numer. Simul. (IF 1.467) Pub Date : 2020-12-17 Sunday C. Eze
In this contribution, a non-linear arctic sea-ice model of fractional Duffing oscillator is given. The solution of the model was obtained using a new proposed analytical method, which is an elegant combination of asymptotic and Laplace methods. The result obtained showed that this method is a very powerful and efficient technique for finding the analytical solution of nonlinear fractional differential
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Numerical investigation of the solutions of Schrödinger equation with exponential cubic B-spline finite element method Int. J. Nonlinear Sci. Numer. Simul. (IF 1.467) Pub Date : 2020-12-16 Ozlem Ersoy Hepson; Idris Dag
In this paper, we investigate the numerical solutions of the cubic nonlinear Schrödinger equation via the exponential cubic B-spline collocation method. Crank–Nicolson formulas are used for time discretization of the target equation. A linearization technique is also employed for the numerical purpose. Four numerical examples related to single soliton, collision of two solitons that move in opposite
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Solving a linear fractional equation with nonlocal boundary conditions based on multiscale orthonormal bases method in the reproducing kernel space Int. J. Nonlinear Sci. Numer. Simul. (IF 1.467) Pub Date : 2020-12-16 Wei Jiang; Zhong Chen; Ning Hu; Yali Chen
In recent years, the study of fractional differential equations has become a hot spot. It is more difficult to solve fractional differential equations with nonlocal boundary conditions. In this article, we propose a multiscale orthonormal bases collocation method for linear fractional-order nonlocal boundary value problems. In algorithm construction, the solution is expanded by the multiscale orthonormal
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Analytical predictor–corrector entry guidance for hypersonic gliding vehicles Int. J. Nonlinear Sci. Numer. Simul. (IF 1.467) Pub Date : 2020-12-15 Huatao Chen; Kun Zhao; Juan L.G. Guirao; Dengqing Cao
For the entry guidance problem of hypersonic gliding vehicles (HGVs), an analytical predictor–corrector guidance method based on feedback control of bank angle is proposed. First, the relative functions between the velocity, bank angle and range-to-go are deduced, and then, the analytical relation is introduced into the predictor–corrector algorithm, which is used to replace the traditional method
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A note on optimal systems of certain low-dimensional Lie algebras Int. J. Nonlinear Sci. Numer. Simul. (IF 1.467) Pub Date : 2020-12-16 Manjit Singh; Rajesh Kumar Gupta
Optimal classifications of Lie algebras of some well-known equations under their group of inner automorphism are re-considered. By writing vector fields of some known Lie algebras in the abstract format, we have proved that there exist explicit isomorphism between Lie algebras and sub-algebras which have already been classified. The isomorphism between Lie algebras is useful in the sense that the classifications
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Research on the vibro-acoustic propagation characteristics of a large mining two-stage planetary gear reducer Int. J. Nonlinear Sci. Numer. Simul. (IF 1.467) Pub Date : 2020-12-16 Wei Yang; Xiaolin Tang
In this paper, a computational model is proposed to predict the noise radiation of a planetary gear reducer. In addition, a system-level vibro-acoustic model of a two-stage planetary gear reducer is also established, and the dynamic contact equations of engagement are deduced to investigate the dynamic loads at the interface of bearing-housing and ring-housing in operation, using a large mining two-stage
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Wavelet-optimized compact finite difference method for convection–diffusion equations Int. J. Nonlinear Sci. Numer. Simul. (IF 1.467) Pub Date : 2020-12-03 Mani Mehra; Kuldip Singh Patel; Ankita Shukla
In this article, compact finite difference approximations for first and second derivatives on the non-uniform grid are discussed. The construction of diffusion wavelets using compact finite difference approximation is presented. Adaptive grids are obtained for non-smooth functions in one and two dimensions using diffusion wavelets. High-order accurate wavelet-optimized compact finite difference (WOCFD)
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Frontmatter Int. J. Nonlinear Sci. Numer. Simul. (IF 1.467) Pub Date : 2020-11-30
Journal Name: International Journal of Nonlinear Sciences and Numerical Simulation Volume: 21 Issue: 7-8 Pages: i-iv
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Stress wave propagation in different number of fissured rock mass based on nonlinear analysis Int. J. Nonlinear Sci. Numer. Simul. (IF 1.467) Pub Date : 2020-11-20 Xiaoming Lou; Mingwu Sun; Jin Yu
The fissures are ubiquitous in deep rock masses, and they are prone to instability and failure under dynamic loads. In order to study the propagation attenuation of dynamic stress waves in rock mass with different number of fractures under confining pressure, nonlinear theoretical analysis, indoor model test and numerical simulation are used respectively. The theoretical derivation is based on displacement
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Noninstantaneous impulsive and nonlocal Hilfer fractional stochastic integrodifferential equations with fractional Brownian motion and Poisson jumps Int. J. Nonlinear Sci. Numer. Simul. (IF 1.467) Pub Date : 2020-11-16 Hamdy M. Ahmed; Mahmoud M. El-Borai; Mohamed E. Ramadan
In this paper, we introduce the mild solution for a new class of noninstantaneous and nonlocal impulsive Hilfer fractional stochastic integrodifferential equations with fractional Brownian motion and Poisson jumps. The existence of the mild solution is derived for the considered system by using fractional calculus, stochastic analysis and Sadovskii’s fixed point theorem. Finally, an example is also
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Distributed consensus of multi-agent systems with increased convergence rate Int. J. Nonlinear Sci. Numer. Simul. (IF 1.467) Pub Date : 2020-11-11 Ke-cai Cao; Yun Chai; Chenglin Liu
Consensus problem with faster convergence rate of consensus problem has been considered in this paper. Adding more edges such as that connecting each agent and its second-nearest neighbor or changing the consensus protocol such as mixing asymptotic terms and terms of finite-time has been proved to be possible ways in increasing the convergence rate of multi-agent system in this paper. Based on analysis
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Dynamic behavior of a stochastic SIRS model with two viruses Int. J. Nonlinear Sci. Numer. Simul. (IF 1.467) Pub Date : 2020-11-10 Jiandong Zhao; Tonghua Zhang; Zhixia Han
To study the effect of environmental noise on the spread of the disease, a stochastic Susceptible, Infective, Removed and Susceptible (SIRS) model with two viruses is introduced in this paper. Sufficient conditions for global existence of positive solution and stochastically asymptotic stability of disease-free equilibrium in the model are given. Then, it is shown that the positive solution is stochastically
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Drive-train selection criteria for n-dof manipulators: basis for modular serial robots library Int. J. Nonlinear Sci. Numer. Simul. (IF 1.467) Pub Date : 2020-11-10 Ekta Singla; Satwinder Singh; Ashish Singla
Towards planning a modular library for customized designs of serial manipulators, a trade-off is required between minimum modules inventory and maximum robotic applications to be handled. This paper focusses at the types of modules which are majorly based upon optimized payload capacity of the modular links. To find minimum types of modules in the modular library, an exercise has been performed on
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Positive periodic solution for inertial neural networks with time-varying delays Int. J. Nonlinear Sci. Numer. Simul. (IF 1.467) Pub Date : 2020-11-10 Feng Duan; Bo Du
In this paper the problems of the existence and stability of positive periodic solutions of inertial neural networks with time-varying delays are discussed by the use of Mawhin’s continuation theorem and Lyapunov functional method. Some sufficient conditions are obtained for guaranteeing the existence and stability of positive periodic solutions of the considered system. Finally, a numerical example
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A new approach to the bienergy and biangle of a moving particle lying in a surface of lorentzian space Int. J. Nonlinear Sci. Numer. Simul. (IF 1.467) Pub Date : 2020-11-11 Talat Körpınar; Yasin Ünlütürk
In this research, we study bienergy and biangles of moving particles lying on the surface of Lorentzian 3-space by using their energy and angle values. We present the geometrical characterization of bienergy of the particle in Darboux vector fields depending on surface. We also give the relationship between bienergy of the surface curve and bienergy of the elastic surface curve. We conclude the paper
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Stability analysis of almost periodic solutions for discontinuous bidirectional associative memory (BAM) neural networks with discrete and distributed delays Int. J. Nonlinear Sci. Numer. Simul. (IF 1.467) Pub Date : 2020-11-11 Weijun Xie; Fanchao Kong; Hongjun Qiu; Xiangying Fu
This paper aims to discuss a class of discontinuous bidirectional associative memory (BAM) neural networks with discrete and distributed delays. By using the set-valued map, differential inclusions theory and fundamental solution matrix, the existence of almost-periodic solutions for the addressed neural network model is firstly discussed under some new conditions. Subsequently, based on the non-smooth
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Robust stabilization control of a spatial inverted pendulum using integral sliding mode controller Int. J. Nonlinear Sci. Numer. Simul. (IF 1.467) Pub Date : 2020-11-11 Ishan Chawla; Vikram Chopra; Ashish Singla
From the last few decades, inverted pendulums have become a benchmark problem in dynamics and control theory. Due to their inherit nature of nonlinearity, instability and underactuation, these are widely used to verify and implement emerging control techniques. Moreover, the dynamics of inverted pendulum systems resemble many real-world systems such as segways, humanoid robots etc. In the literature
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Analysis of (α, β)-order coupled implicit Caputo fractional differential equations using topological degree method Int. J. Nonlinear Sci. Numer. Simul. (IF 1.467) Pub Date : 2020-11-12 Usman Riaz; Akbar Zada
This article is devoted to establish the existence of solution of (α,β)-order coupled implicit fractional differential equation with initial conditions, using Laplace transform method. The topological degree theory is used to obtain sufficient conditions for uniqueness and at least one solution of the considered system. Beside this, Ulam’s type stabilities are discussed for the proposed system. To
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Optimization approach to the constrained regulation problem for linear continuous-time fractional-order systems Int. J. Nonlinear Sci. Numer. Simul. (IF 1.467) Pub Date : 2020-11-12 Xindong Si; Hongli Yang
This paper deals with the Constrained Regulation Problem (CRP) for linear continuous-times fractional-order systems. The aim is to find the existence conditions of linear feedback control law for CRP of fractional-order systems and to provide numerical solving method by means of positively invariant sets. Under two different types of the initial state constraints, the algebraic condition guaranteeing
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Systematic formulation of a general numerical framework for solving the two-dimensional convection–diffusion–reaction system Int. J. Nonlinear Sci. Numer. Simul. (IF 1.467) Pub Date : 2020-11-12 Aswin V. Sugathan; Ashish Awasthi
A general numerical framework is designed for the two-dimensional convection–diffusion–reaction (CDR) system. The compatibility of differential quadrature and finite difference methods (FDM) are utilized for the formulation. The idea is to switch one numerical scheme to another numerical scheme without changing the formulation. The only requirement is to input the weighting coefficients associated
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Existence and uniqueness of solutions of nonlinear fractional order problems via a fixed point theorem Int. J. Nonlinear Sci. Numer. Simul. (IF 1.467) Pub Date : 2020-11-05 Zahra Ahmadi; Rahmatollah Lashkaripour; Hamid Baghani; Shapour Heidarkhani
In this paper, we introduce an Caputo fractional high-order problem with a new boundary condition including two orders γ∈(n1−1,n1] and η∈(n2−1,n2] for any n1,n2∈ℕ. We deals with existence and uniqueness of solutions for the problem. The approach is based on the Krasnoselskii’s fixed point theorem and contraction mapping principle. Moreover, we present several examples to show the clarification and
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Bell-shaped soliton solutions and travelling wave solutions of the fifth-order nonlinear modified Kawahara equation Int. J. Nonlinear Sci. Numer. Simul. (IF 1.467) Pub Date : 2020-11-06 Ali Başhan
The main aim of this work is to investigate numerical solutions of the two different types of the fifth-order modified Kawahara equation namely bell-shaped soliton solutions and travelling wave solutions that occur thereby the different type of the Korteweg–de Vries equation. For this approach, we have used an effective and simple type of finite difference method namely Crank-Nicolson scheme for time
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Numerical solution for the fractional-order one-dimensional telegraph equation via wavelet technique Int. J. Nonlinear Sci. Numer. Simul. (IF 1.467) Pub Date : 2020-11-05 Kumbinarasaiah Srinivasa; Hadi Rezazadeh
In this article, we proposed an efficient numerical technique for the solution of fractional-order (1 + 1) dimensional telegraph equation using the Laguerre wavelet collocation method. Some examples are illustrated to inspect the efficiency of the proposed technique and convergence analysis is discussed in terms of a theorem. Here, the fractional-order telegraph equation is converted into a system
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Rotorcraft fuselage/main rotor coupling dynamics modelling and analysis Int. J. Nonlinear Sci. Numer. Simul. (IF 1.467) Pub Date : 2020-11-04 Salvador Castillo-Rivera; Maria Tomas-Rodriguez
This article presents the fuselage/main rotor coupling dynamics under a modal analysis to study the modes of oscillation. The authors provide a rotorcraft simulation model that captures complex dynamics, wherein the validation is done with existing theories. The model has been set up by using VehicleSim, software specialized in modelling mechanical systems composed by rigid bodies. It is presented
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Norm inequalities on variable exponent vanishing Morrey type spaces for the rough singular type integral operators Int. J. Nonlinear Sci. Numer. Simul. (IF 1.467) Pub Date : 2020-10-27 Ferit Gürbüz; Shenghu Ding; Huili Han; Pinhong Long
In this paper, applying the properties of variable exponent analysis and rough kernel, we study the mapping properties of rough singular integral operators. Then, we show the boundedness of rough Calderón–Zygmund type singular integral operator, rough Hardy–Littlewood maximal operator, as well as the corresponding commutators in variable exponent vanishing generalized Morrey spaces on bounded sets
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Existence, stability and controllability results of fractional dynamic system on time scales with application to population dynamics Int. J. Nonlinear Sci. Numer. Simul. (IF 1.467) Pub Date : 2020-10-29 Vipin Kumar; Muslim Malik
In this manuscript, we investigate the existence, uniqueness, Hyer-Ulam stability and controllability analysis for a fractional dynamic system on time scales. Mainly, this manuscript has three segments: In the first segment, we give the existence of solutions. The second segment is devoted to the study of stability analysis while in the last segment, we establish the controllability results. We use
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Bifurcation, routes to chaos, and synchronized chaos of electromagnetic valve train in camless engines Int. J. Nonlinear Sci. Numer. Simul. (IF 1.467) Pub Date : 2020-10-21 Shun-Chang Chang
The main objects of this paper focus on the complex dynamics and chaos control of an electromagnetic valve train (EMV). A variety of periodic solutions and nonlinear phenomena can be expressed using various numerical techniques such as time responses, phase portraits, Poincaré maps, and frequency spectra. The effects of varying the system parameters can be observed in the bifurcation diagram. It shows
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Research on prediction model of thermal and moisture comfort of underwear based on principal component analysis and Genetic Algorithm–Back Propagation neural network Int. J. Nonlinear Sci. Numer. Simul. (IF 1.467) Pub Date : 2020-10-21 Pengpeng Cheng; Daoling Chen; Jianping Wang
In order to improve the efficiency and accuracy of thermal and moisture comfort prediction of underwear, a new prediction model is designed by using principal component analysis method to reduce the dimension of related variables and eliminate the multi-collinearity relationship between variables, and then inputting the converted variables into genetic algorithm (GA) and BP neural network. In order
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New technique for the approximation of the zeros of nonlinear scientific models Int. J. Nonlinear Sci. Numer. Simul. (IF 1.467) Pub Date : 2020-10-23 Faisal Ali; Waqas Aslam; Shuliang Huang
Most of the problems in mathematical and engineering sciences can be studied in the context of nonlinear equations. In this paper, we develop a new family of iterative methods for the approximation of the zeros of mathematical models whose governing equations are nonlinear in nature. The proposed methods are based on decomposition technique due to Daftardar-Gejji and Jaffri [1]. The new family gives
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Algebro-geometric constructions of the Heisenberg hierarchy Int. J. Nonlinear Sci. Numer. Simul. (IF 1.467) Pub Date : 2020-10-23 Zhu Li
The Heisenberg hierarchy and its Hamiltonian structure are derived respectively by virtue of the zero-curvature equation and the trace identity. With the help of the Lax matrix, we introduce an algebraic curve Kn of arithmetic genus n, from which we define meromorphic function ϕ and straighten out all of the flows associated with the Heisenberg hierarchy under the Abel–Jacobi coordinates. Finally,
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Frontmatter Int. J. Nonlinear Sci. Numer. Simul. (IF 1.467) Pub Date : 2020-10-12
Journal Name: International Journal of Nonlinear Sciences and Numerical Simulation Volume: 21 Issue: 6 Pages: i-iii
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Nonlocal fractional semilinear differential inclusions with noninstantaneous impulses and of order α ∈ (1, 2) Int. J. Nonlinear Sci. Numer. Simul. (IF 1.467) Pub Date : 2020-10-01 JinRong Wang; Ahmed G. Ibrahim; Donal O’Regan; Adel A. Elmandouh
In this paper, we establish the existence of mild solutions for nonlocal fractional semilinear differential inclusions with noninstantaneous impulses of order α ∈ (1,2) and generated by a cosine family of bounded linear operators. Moreover, we show the compactness of the solution set. We consider both the case when the values of the multivalued function are convex and nonconvex. Examples are given
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Numerical study of the coefficient identification algorithm based on ensembles of adjoint problem solutions for a production-destruction model Int. J. Nonlinear Sci. Numer. Simul. (IF 1.467) Pub Date : 2020-09-29 Alexey V. Penenko; Zhadyra S. Mukatova; Akzhan B. Salimova
A numerical algorithm for the solution of an inverse coefficient problem for nonstationary, nonlinear production-destruction type model is proposed and tested on an example of the Lorenz’63 system. With an ensemble of adjoint problem solutions, the inverse problem is transformed into a quasi-linear matrix problem and solved with Newton-type algorithm. Two different ways of the adjoint ensemble construction
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Ground state solutions for nonlinear fractional Kirchhoff–Schrödinger–Poisson systems Int. J. Nonlinear Sci. Numer. Simul. (IF 1.467) Pub Date : 2020-09-23 Li Wang; Tao Han; Kun Cheng; Jixiu Wang
In this paper, we study the existence of ground state solutions for the following fractional Kirchhoff–Schrödinger–Poisson systems with general nonlinearities: {(a+b[u]s2) (−Δ)su+u+ϕ(x)u=(|x|−μ∗F(u))f(u)in ℝ3 ,(−Δ)tϕ(x)=u2in ℝ3 ,where [u]s2=∫ℝ3|(−Δ)s2u|2 dx=∬ℝ3×ℝ3|u(x)−u(y)|2|x−y|3+2s dxdy ,s,t∈(0,1) with 2t+4s>3,0<μ<3−2t,f:ℝ3×ℝ→ℝ satisfies a Carathéodory condition and (−Δ)s is the fractional Laplace
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Existence and uniqueness of solutions for coupled systems of Liouville-Caputo type fractional integrodifferential equations with Erdélyi-Kober integral conditions Int. J. Nonlinear Sci. Numer. Simul. (IF 1.467) Pub Date : 2020-09-23 Muthaiah Subramanian; Akbar Zada
In this paper, we examine a coupled system of fractional integrodifferential equations of Liouville-Caputo form with nonlinearities depending on the unknown functions, as well as their lower-order fractional derivatives and integrals supplemented with coupled nonlocal and Erdélyi-Kober fractional integral boundary conditions. We explain that the topic discussed in this context is new and gives more
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Optimization of exact controllability for fractional impulsive partial stochastic differential systems via analytic sectorial operators Int. J. Nonlinear Sci. Numer. Simul. (IF 1.467) Pub Date : 2020-09-25 Zuomao Yan; Yong-Hui Zhou
In this paper, we consider the optimization problems of exact controllability for a new class of fractional impulsive partial stochastic differential systems with state-dependent delay in Hilbert spaces. By utilizing suitable fixed point approach without imposing severe compactness condition on the operators, the theory of analytic sectorial operators, stochastic analysis, and the Hausdorff measure
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Parallel iterative finite-element algorithms for the Navier–Stokes equations with nonlinear slip boundary conditions Int. J. Nonlinear Sci. Numer. Simul. (IF 1.467) Pub Date : 2020-09-23 Kangrui Zhou; Yueqiang Shang
Based on full domain partition, three parallel iterative finite-element algorithms are proposed and analyzed for the Navier–Stokes equations with nonlinear slip boundary conditions. Since the nonlinear slip boundary conditions include the subdifferential property, the variational formulation of these equations is variational inequalities of the second kind. In these parallel algorithms, each subproblem
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A reliable numerical approach for nonlinear fractional optimal control problems Int. J. Nonlinear Sci. Numer. Simul. (IF 1.467) Pub Date : 2020-09-24 Harendra Singh; Rajesh K. Pandey; Devendra Kumar
In this work, we study a numerical approach for studying a nonlinear model of fractional optimal control problems (FOCPs). We have taken the fractional derivative in a dynamical system of FOCPs, which is in Liouville–Caputo sense. The presented scheme is a grouping of an operational matrix of integrations for Jacobi polynomials and the Ritz method. The proposed approach converts the FOCP into a system
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Using the generalized Adams-Bashforth-Moulton method for obtaining the numerical solution of some variable-order fractional dynamical models Int. J. Nonlinear Sci. Numer. Simul. (IF 1.467) Pub Date : 2020-09-23 Mohamed M. Khader
This paper is devoted to introduce a numerical treatment using the generalized Adams-Bashforth-Moulton method for some of the variable-order fractional modeling dynamics problems, such as Riccati and Logistic differential equations. The fractional derivative is described in Caputo variable-order fractional sense. The obtained numerical results of the proposed models show the simplicity and efficiency
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Synchronization of Cohen-Grossberg fuzzy cellular neural networks with time-varying delays Int. J. Nonlinear Sci. Numer. Simul. (IF 1.467) Pub Date : 2020-09-17 Munia Samy Manikandan; Kurunathan Ratnavelu; Pagavathigounder Balasubramaniam; Seng Huat Ong
In this paper, a class of Cohen-Grossberg fuzzy cellular neural networks (CGFCNNs) with time-varying delays are considered. Initially, the sufficient conditions are proposed to ascertain the existence and uniqueness of the solutions for the considered dynamical system via homeomorphism mapping principle. Then synchronization of the considered delayed neural networks is analyzed by utilizing the drive-response
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Synchronization stability on the BAM neural networks with mixed time delays Int. J. Nonlinear Sci. Numer. Simul. (IF 1.467) Pub Date : 2020-09-18 Ahmadjan Muhammadhaji; Zhidong Teng
This article investigates the general decay synchronization (GDS) for the bidirectional associative memory neural networks (BAMNNs). Compared with previous research results, both time-varying delays and distributed time delays are taken into consideration. By using Lyapunov method and using useful inequality techniques, some sufficient conditions on the GDS for BAMNNs are derived. Finally, a numerical
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Application of Hermite–Padé approximation for detecting singularities of some boundary value problems Int. J. Nonlinear Sci. Numer. Simul. (IF 1.467) Pub Date : 2020-09-18 Youness Filali; Mustapha Er-Riani; Mustapha EL Jarroudi
A computational approach to the investigation of bifurcations, based on the use of a special type of Hermite–Padé approximant, is presented. The first part of this study is a review of a singularity extraction technique based on the assumption that the given series is the local representation of an algebraic function in the independent variable. The principal merit of the procedure is its ability to
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Solvability of fractional differential inclusions with nonlocal initial conditions via resolvent family of operators Int. J. Nonlinear Sci. Numer. Simul. (IF 1.467) Pub Date : 2020-09-18 Yong-Kui Chang; Rodrigo Ponce; Xu-Sheng Yang
In this paper, we consider mild solutions to fractional differential inclusions with nonlocal initial conditions. The main results are proved under conditions that (i) the multivalued term takes convex values with compactness of resolvent family of operators; (ii) the multivalued term takes nonconvex values with compactness of resolvent family of operators and (iii) the multivalued term takes nonconvex
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Nonlinear solution of the reaction–diffusion equation using a two-step third–fourth-derivative block method Int. J. Nonlinear Sci. Numer. Simul. (IF 1.467) Pub Date : 2020-09-15 Oluwaseun Adeyeye; Ali Aldalbahi; Jawad Raza; Zurni Omar; Mostafizur Rahaman; Mohammad Rahimi-Gorji; Nguyen Minh Hoang
The processes of diffusion and reaction play essential roles in numerous system dynamics. Consequently, the solutions of reaction–diffusion equations have gained much attention because of not only their occurrence in many fields of science but also the existence of important properties and information in the solutions. However, despite the wide range of numerical methods explored for approximating
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The extended auxiliary equation mapping method to determine novel exact solitary wave solutions of the nonlinear fractional PDEs Int. J. Nonlinear Sci. Numer. Simul. (IF 1.467) Pub Date : 2020-09-16 Jalil Manafian; Onur Alp Ilhan; Laleh Avazpour
In this paper, some new nonlinear fractional partial differential equations (PDEs) have been considered.Three models are including the space-time fractional-order Boussinesq equation, space-time (2 + 1)-dimensional breaking soliton equations, and space-time fractional-order SRLW equation describe the behavior of these equations in the diverse applications. Meanwhile, the fractional derivatives in the
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A numerical technique for a general form of nonlinear fractional-order differential equations with the linear functional argument Int. J. Nonlinear Sci. Numer. Simul. (IF 1.467) Pub Date : 2020-09-17 Khalid K. Ali; Mohamed A. Abd El salam; Emad M. H. Mohamed
In this paper, a numerical technique for a general form of nonlinear fractional-order differential equations with a linear functional argument using Chebyshev series is presented. The proposed equation with its linear functional argument represents a general form of delay and advanced nonlinear fractional-order differential equations. The spectral collocation method is extended to study this problem
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Stability control of a novel multidimensional fractional-order financial system with time‐delay via impulse control Int. J. Nonlinear Sci. Numer. Simul. (IF 1.467) Pub Date : 2020-08-25 Zhe Zhang; Jing Zhang; Fan Yong Cheng; Feng Liu; Can Ding
This paper is concerned about the impulsive control of a class of novel nonlinear fractional-order financial system with time-delay. Considering the variation of every states in the fractional-order financial system in the real world has certain delay for various reasons, thus we add corresponding delay on every state variable. Different from the traditional method of stability judgment, we choose
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The monotone iterative method for the integral boundary value problems of fractional p-Laplacian equations with delay Int. J. Nonlinear Sci. Numer. Simul. (IF 1.467) Pub Date : 2020-08-25 Chunyan Wei; Xiping Liu; Mei Jia; Luchao Zhang
Based on the theory of lower and upper solutions, we study the monotone iterative method for the nonlinear integral boundary value problems of fractional p-Laplacian equations with delay, which involves both Riemann–Liouville derivative and Caputo derivative. Some new results on the existence of positive solutions are established and the iterative methods for finding approximate solutions of the boundary
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Approximate controllability of fractional stochastic evolution equations with nonlocal conditions Int. J. Nonlinear Sci. Numer. Simul. (IF 1.467) Pub Date : 2020-08-24 Yonghong Ding; Yongxiang Li
This paper deals with the approximate controllability for a class of fractional stochastic evolution equations with nonlocal initial conditions in a Hilbert space. We delete the compactness condition or Lipschitz condition for nonlocal term appearing in various literatures, and only need to suppose some weak growth condition on the nonlocal term. The discussion is based on the fixed point theorem,
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Synchronization control between discrete uncertain networks with different topologies Int. J. Nonlinear Sci. Numer. Simul. (IF 1.467) Pub Date : 2020-08-24 Ling Lü; Cunming Zou; Fuli Zhang
Based on open-loop–closed-loop technology, we researched the outer synchronization between discrete uncertain networks with different topologies. In order to make the drive and response networks realize the synchronization, a special Lyapunov function is constructed and the open-loop–closed-loop controller is designed. At the same time, we designed an effective parameter identification law to accurately
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Optical solitons and stability analysis for the generalized second-order nonlinear Schrödinger equation in an optical fiber Int. J. Nonlinear Sci. Numer. Simul. (IF 1.467) Pub Date : 2020-08-17 Nauman Raza; Saima Arshed; Ahmad Javid
In this paper, the generalized second-order nonlinear Schrödinger equation with light-wave promulgation in an optical fiber, is studied for optical soliton solutions. Three analytical methods such as the exp(−ϕ(χ))-expansion method, the G′/G2-expansion method and the first integral methods are used to extract dark, singular, periodic, dark-singular combo optical solitons for the proposed model. These
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Approximate controllability of nonlinear Hilfer fractional stochastic differential system with Rosenblatt process and Poisson jumps Int. J. Nonlinear Sci. Numer. Simul. (IF 1.467) Pub Date : 2020-08-18 Subramaniam Saravanakumar; Pagavathigounder Balasubramaniam
This manuscript is concerned with the approximate controllability problem of Hilfer fractional stochastic differential system (HFSDS) with Rosenblatt process and Poisson jumps. We derive the main results in stochastic settings by employing analytic resolvent operators, fractional calculus and fixed point theory. Further, we express the theoretical result with an example.
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On the behaviors of rough multilinear fractional integral and multi-sublinear fractional maximal operators both on product Lp and weighted Lp spaces Int. J. Nonlinear Sci. Numer. Simul. (IF 1.467) Pub Date : 2020-08-12 Ferit Gürbüz
The aim of this paper is to get the product Lp-estimates, weighted estimates and two-weighted estimates for rough multilinear fractional integral operators and rough multi-sublinear fractional maximal operators, respectively. The author also studies two-weighted weak type estimate on product Lp(ℝn) for rough multi-sublinear fractional maximal operators. In fact, this article is the rough kernel versions
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Fractional (3+1)-dim Jimbo Miwa system: invariance properties, exact solutions, solitary pattern solutions and conservation laws Int. J. Nonlinear Sci. Numer. Simul. (IF 1.467) Pub Date : 2020-08-10 Sachin Kumar; Baljinder Kour
The present article is devoted to scouting invariant analysis and some kind of approximate and explicit solutions of the (3+1)-dimensional Jimbo Miwa system of nonlinear fractional partial differential equations (NLFPDEs). Feasible vector field of the system is obtained by employing the invariance attribute of one-parameter Lie group of transformation. The reduction of the number of independent variables
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Periodic solutions for stochastic Cohen–Grossberg neural networks with time-varying delays Int. J. Nonlinear Sci. Numer. Simul. (IF 1.467) Pub Date : 2020-08-10 Wanqin Wu; Li Yang; Yaping Ren
This paper is concerned with the periodic solutions for a class of stochastic Cohen–Grossberg neural networks with time-varying delays. Since there is a non-linearity in the leakage terms of stochastic Cohen–Grossberg neural networks, some techniques are needed to overcome the difficulty in dealing with the nonlinearity. By applying fixed points principle and Gronwall–Bellman inequality, some sufficient
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Lie symmetries and singularity analysis for generalized shallow-water equations Int. J. Nonlinear Sci. Numer. Simul. (IF 1.467) Pub Date : 2020-08-10 Andronikos Paliathanasis
We perform a complete study by using the theory of invariant point transformations and the singularity analysis for the generalized Camassa-Holm (CH) equation and the generalized Benjamin-Bono-Mahoney (BBM) equation. From the Lie theory we find that the two equations are invariant under the same three-dimensional Lie algebra which is the same Lie algebra admitted by the CH equation. We determine the
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Global exponential stability analysis of anti-periodic solutions of discontinuous bidirectional associative memory (BAM) neural networks with time-varying delays Int. J. Nonlinear Sci. Numer. Simul. (IF 1.467) Pub Date : 2020-08-10 Xiangying Fu; Fanchao Kong
This paper is concerned with a class of bidirectional associative memory (BAM) neural networks with discontinuous activations and time-varying delays. Under the basic framework of differential inclusions theory, the existence result of solutions in sense of Filippov solution is firstly established by using the fundamental solution matrix of coefficients and inequality analysis technique. Also, the
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A multivariate spectral quasi-linearization method for the solution of (2+1) dimensional Burgers’ equations Int. J. Nonlinear Sci. Numer. Simul. (IF 1.467) Pub Date : 2020-08-10 Phumlani G. Dlamini; Vusi M. Magagula
In this paper, we introduce the multi-variate spectral quasi-linearization method which is an extension of the previously reported bivariate spectral quasi-linearization method. The method is a combination of quasi-linearization techniques and the spectral collocation method to solve three-dimensional partial differential equations. We test its applicability on the (2 + 1) dimensional Burgers’ equations
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The barotropic Rossby waves with topography on the earth’s δ-surface Int. J. Nonlinear Sci. Numer. Simul. (IF 1.467) Pub Date : 2020-08-10 Jian Song; ShaoXia Liu
The Rossby solitary waves in the barotropic vorticity model which contains the topography on the earth’s δ-surface is investigated. First, applying scale analysis method, obtained the generalized quasi-geostrophic potential vorticity equation (QGPVE). Using The Wentzel–Kramers–Brillouin (WKB) theory, the evolution equation of Rossby waves is the variable-coefficient Korteweg–de Vries (KdV) equation