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

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

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

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

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

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,

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

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

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.

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

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

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

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

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

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

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

In this paper, the generalized nonlinear Schrödinger equation with variable coefficients (gvcNLSE) arising in optical fiber is solved by using two different techniques the trail equation method and direct integration method. Many different new types of wave solutions like Jacobi, periodic and soliton wave solutions are obtained. From this study we have concluded that the direct integration method is

In this paper, we propose a hybrid parallel programming approach for a numerical solution of a two-dimensional acoustic wave equation using an implicit difference scheme for a single computer. The calculations are carried out in an implicit finite difference scheme. First, we transform the differential equation into an implicit finite-difference equation and then using the alternating direction implicit

For a second-order nonlinear singularly perturbed boundary value problem (SPBVP), we develop two novel algorithms to find the solution, which automatically satisfies the Robin boundary conditions. For the highly singular nonlinear SPBVP the Robin boundary functions are hard to be fulfilled exactly. In the paper we first introduce the new idea of boundary shape function (BSF), whose existence is proven

We study a system of particles in a two-dimensional geometry that move according to a reinforced random walk with transition probabilities dependent on the solutions of reaction-diffusion equations (RDEs) for the underlying fields. A birth process and a history-dependent killing process are also considered. This system models tumor-induced angiogenesis, the process of formation of blood vessels induced

In this work, the effectiveness of the adaptive neural based fuzzy inference system (ANFIS) in identifying underactuated systems is illustrated. Two case studies of underactuated systems are used to validate the system identification i. e., linear inverted pendulum (LIP) and rotary inverted pendulum (RIP). Both the systems are treated as benchmark systems in modeling and control theory for their inherit

We study the Jimbo – Miwa equation and two of its extended forms, as proposed by Wazwaz et al., using Lie’s group approach. Interestingly, the travelling – wave solutions for all the three equations are similar. Moreover, we obtain certain new reductions which are completely different for each of the three equations. For example, for one of the extended forms of the Jimbo – Miwa equation, the subsequent

A weighted companion of Ostrowski type inequality is established. Some sharp inequalities are proved. Application to a quadrature rule is provided.

We derive two iterative methods with memory for approximating a simple root of any nonlinear equation. For this purpose, we take two optimal methods without memory of order four and eight and convert them into the methods with memory without increasing any further function evaluation. These methods involve a self-accelerator (parameter) that depends upon the iteration index to increase the order of

In this paper, the matters of dissipativity and synchronization for non-autonomous Hopfield neural networks with discontinuous activations are investigated. Firstly, under the framework of extending Filippov differential inclusion theory, several effective new criteria are derived. The global dissipativity of Filippov solution to neural networks is proved by using generalized Halanay inequality and

In this communication, we show that a family of partial differential equations such as the linear and nonlinear wave equations propagating in an inhomogeneous medium may be derived if the action functional is replaced by a new functional characterized by two occurrences of integrals where the integrands are non-standard singular Lagrangians. Several features are illustrated accordingly.

Fractional calculus has been shown to improve the dynamics of differential system models and provide a better understanding of their dynamics. This paper considers the time–fractional version of the Degn–Harrison reaction–diffusion model. Sufficient conditions are established for the local and global asymptotic stability of the model by means of invariant rectangles, the fundamental stability theory

This paper studies the (3 + 1)-dimensional generalized Kadomtsev–Petviashvili–Boussinesq (KPB) equation via the Hirota’s bilinear form and symbolic computation. Mixed type lump solutions are presented, which include rational function, trigonometric function and hyperbolic function. The propagation and the dynamical behaviors of these mixed type of lump solutions are shown by some three-dimensional

By using critical point theory, some new existence results of at least one periodic solution with minimal period pM for fourth-order nonlinear difference equations are obtained. Our approach used in this paper is a variational method.

To analysis the failure and energy absorption of carbon fiber reinforced polymer (CFRP) thin-walled square tube, the quasi-static axial compression loading tests are conducted for [±45]3s square tube, and the square tube after test is scanned to further investigate the failure mechanism. Three different finite element models, i.e. single-layer shell model, multi-layer shell model and stacked shell

There have appeared in the literature a lot of optimal eighth-order iterative methods for approximating simple zeros of nonlinear functions. Although, the similar ideas can be extended for the case of multiple zeros but the main drawback is that the order of convergence and computational efficiency reduce dramatically. Therefore, in order to retain the accuracy and convergence order, several optimal

Journal Name: International Journal of Nonlinear Sciences and Numerical Simulation Volume: 21 Issue: 3-4 Pages: i-iii

In this work, we established new travelling wave solutions for some nonlinear evolution equations with dual-power-law nonlinearity namely the Zakharov–Kuznetsov equation, the Benjamin–Bona–Mahony equation and the Korteweg–de Vries equation. The functional variable method was used to construct travelling wave solutions of nonlinear evolution equations with dual-power-law nonlinearity. The travelling

In this paper, we present a numerical simulation of a round impacting jet using coupled Smoothed Particle Hydrodynamics (SPH) and Finite Element (FE) methods. Numerical results are compared with the results of another simulation carried out by the CEL (Coupled Eulerian-Lagrangian) method. A water jet with a spherical head was used at an initial speed of 570 m/s to impact a flat plate made of Polymethyl-Methacrylate

We study a fractional integro-differential equation subject to multi-point boundary conditions: D0+αu(t)+f(t,u(t),Tu(t),Su(t))=b, t∈(0,1),u(0)=u′(0)=⋯=u(n−2)(0)=0,D0+pu(t)|t=1=∑i=1maiD0+qu(t)|t=ξi,

In this paper, we concern with the existence of mild solution to nonlocal initial value problem for nonlinear Sobolev-type impulsive evolution equations with Hilfer fractional derivative which generalized the Riemann–Liouville fractional derivative. At first, we establish an equivalent integral equation for our main problem. Second, by means of the properties of Hilfer fractional calculus, combining

We consider the existence, uniqueness and Ulam–Hyers–Rassias stability of solutions to the initial value problem with noninstantaneous impulses on ordered Banach spaces. The existence and uniqueness of solutions for nonlinear ordinary differential equation with noninstantaneous impulses is obtained by using perturbation technique, monotone iterative method and a new estimation technique of the measure

In the present study, we dilate the differential transform scheme to develop a reliable scheme for studying analytically the mutual impact of temporal and spatial fractional derivatives in Caputo’s sense. We also provide a mathematical framework for the transformed equations of some fundamental functional forms in fractal 2-dimensional space. To demonstrate the effectiveness of our proposed scheme

This paper considers a Hantavirus infection model consisting of a system of fractional-order ordinary differential equations with logistic growth. The fractional-order model describes the spread of Hantavirus infection in a system consisting of a population of susceptible and infected mice. The existence, uniqueness, non-negativity and boundedness of the solutions are established. In addition, the

This paper applies the Euler and the fourth-order Runge–Kutta methods in the analysis of fractional order dynamical systems. In order to illustrate the two techniques, the numerical algorithms are applied in the solution of several fractional attractors, namely the Lorenz, Duffing and Liu systems. The algorithms are implemented with the aid of Mathematica symbolic package. Furthermore, the Lyapunov

In this paper, we constructed the variational principles for Bogoyavlensky–Konopelchenko equation, the generalized (3+1)-dimensional nonlinear wave in liquid containing gas bubbles and a new coupled Kadomtsev–Petviashvili (KP) equation via He’s semi-inverse method. Based on this formulation, we obtained the solitary wave solutions via Ritz method. We explained the properties of the soliton waves numerically

In this paper, we used Henstock–Kurzweil–Pettis integral instead of classical integrals. Using fixed point theorem and weak measure of noncompactness, we study the existence of weak solutions of boundary value problem for fractional integro-differential equations in Banach spaces. Our results generalize some known results. Finally, an example is given to demonstrate the feasibility of our conclusions

A portable pneumatic video-tactile sensor for determining the local stiffness of soft tissue and the methodology for its application are considered. The expected range of local elastic modulus that can be estimated by the sensor is 100 kPa–1 MPa. The current version of the device is designed to determine the characteristics of tissues that are close in mechanical properties to the skin with subcutis

Mass or heat transfer may cause volume variation, and the food hydration model is one of them that undergoes hydration (or drying) conveying volume change. In this paper, the numerical approximate solution based on an integral method has been presented for soybean hydration model. Trace of the moving boundary and unknown moisture content at the center of the grain have been determined. The obtained

This paper studies the dynamics of two fractional-order chaotic maps based on two standard chaotic maps with sine terms. The dynamic behavior of this map is analyzed using numerical tools such as phase plots, bifurcation diagrams, Lyapunov exponents and 0–1 test. With the change of fractional-order, it is shown that the proposed fractional maps exhibit a range of different dynamical behaviors including

Journal Name: International Journal of Nonlinear Sciences and Numerical Simulation Volume: 21 Issue: 2 Pages: i-iii

In this paper, we study an implicit sequential fractional order differential equation with non-instantaneous impulses and multi-point boundary conditions. The article comprehensively elaborate four different types of Ulam’s stability in the lights of generalized Diaz Margolis’s fixed point theorem. Moreover, some sufficient conditions are constructed to observe the existence and uniqueness of solutions

A developed momentum transfer coefficient based on Wen’s 1966 model was proposed, in which the two threshold values were used to keep the continuous particle porosity function. A second-order moment gas–particle two-fluid turbulent model that coupled this coefficient, was established to model and simulate the particle horizontal channel flows. An improved Reynolds stresses transport to close fluctuation

A remanufacturing Cournot duopoly game is introduced based on a nonlinear utility function in this paper. What we mean by remanufacturing here is that the second firm in this game receives used products and remanufacture them and then sell them again in the market. The bounded rationality mechanism is used to form a piecewise system that describes this game in discrete time periods. This piecewise

In this study, a method combined with both Euler polynomials and the collocation method is proposed for solving linear fractional differential equations with delay. The proposed method yields an approximate series solution expressed in the truncated series form in which terms are constituted of unknown coefficients that are to be determined according to Euler polynomials. The matrix method developed

This paper is concerned with the construction of global measure-valued solutions to the extended Riemann problem for a non-strictly hyperbolic system of two conservation laws with delta-type initial data. The wave interaction problems have been extensively studied for all kinds of situations by using the initial condition consisting of constant states in three pieces instead of delta-type initial data

In this paper, the movement of the water surface is numerically simulated when a dam is broken by the volume of fluid (VOF) method. The mathematical model is based on the Navier–Stokes equations and uses the large eddy simulation turbulent model, describing the flow of an incompressible viscous fluid and the equation for the phase. These equations are discretized by the finite-volume method. Numerical

A numerical approach is used herein to study the primary resonant dynamics of functionally graded (FG) cylindrical nanoscale panels taking the strain gradient effects into consideration. The basic relations of the paper are written based upon Mindlin’s strain gradient theory (SGT) and three-dimensional (3D) elasticity. Since the formulation is developed using Mindlin’s SGT, it is possible to reduce

The aim of this work is to establish fixed point theorems under rational type contractions in the framework of complex-valued metric spaces. These theorems extend and generalize some prominent results in the present literature. Furthermore, as an application the existence result is given for the system of Volterra–Hammerstein non-linear integral equations.

This work presents the constrained optimal control of a fractionally damped elastic beam in which the damping characteristic is described with the Caputo fractional derivative of order 1/2. To achieve the optimal control that involves energy optimal control index with fixed endpoints, the fractionally damped elastic beam problem is first converted to a state space form of order 1/2 by using a change

In this article, the differential transform method (DTM) is used to solve the nonlinear boundary value problems describing heat transfer in continuously moving fins undergoing convective-radiative heat dissipation. The thermal conductivity is variable and temperature dependent. The surface of the moving fin is assumed to be gray with a constant emissivity ɛ. The flow in the surrounding medium provides

In this paper, the extended Boiti–Leon–Manna–Pempinelli equation (eBLMP) is first proposed, and by Ma’s [] method, a class of lump and lump–kink soliton solutions is explicitly generated by symbolic computations. The propagation orbit, velocity and extremum of the lump solutions on (x,y) plane are studied in detail. Interaction solutions composed of lump and kink soliton are derived by means of choosing

Air pollution is caused by contamination of air due to various natural and anthropogenic activities. The growing air pollution has diverse adverse effects on human health and other living species. However, a significant reduction in the concentration of air pollutants has been observed during the rainy season. Recently, a number of studies have been performed to understand the mechanism of removal

The unsteady self-similar flow due to a permeable shrinking sheet is analyzed in this investigation. The current theoretical study is enacted in the light of correct self-similar formulation proposed by (Mehmood. A. Viscous flows: Stretching and shrinking of surfaces, Springer, 2017). For the existence of a meaningful solution the retarded boundary-layer developed due to retarded shrinking wall velocity

The Sylvester–Kac matrix, also known as Clement matrix, has many extensions and applications. The evaluation of determinant and spectra of many of its generalizations sometimes are hard to compute. Recently, E. Kılıç and T. Arikan proposed an extension the Sylvester–Kac matrix, where the main diagonal is a 2-periodic sequence. They found its determinant using a spectral technique. In this short note