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

Cournot’s game is one of the most distinguished and influential economic models. However, the classical integer order derivatives utilized in Cournot’s game lack the efficiency to simulate the significant memory characteristics observed in many economic systems. This work aims at introducing a dynamical study of a more realistic proposed competition Cournot-like duopoly game having fractional order

In this article, we study the existence and uniqueness of solutions of a switched coupled implicit ψ-Hilfer fractional differential system. The existence and uniqueness results are obtained by using fixed point techniques. Further, we investigate different kinds of stability such as Hyers–Ulam stability and Hyers–Ulam–Rassias stability. Finally, an example is provided to illustrate the obtained results

A nonlocal elasticity theory is a popular growing technique for mechanical analysis of the micro- and nanoscale structures which captures the small-size effects. In this paper, a comprehensive study was carried out to investigate the influence of the nonlocal parameter on the bifurcation behavior of a capacitive clamped-clamped nano-beam in the presence of the electrostatic and centrifugal forces.

We propose a non-integer order model for the dynamics of the coinfection of HIV and HSV-2. We calculate the reproduction number of the model and study the local stability of the disease-free equilibrium. Simulations of the model for the variation of epidemiologically relevant parameters and the order of the non-integer order derivative, α, reveal interesting dynamics. These results are discussed from

In this work, the (4+1)-dimensional Fokas equation, which is an important physics model, is under investigation. Based on the obtained soliton solutions, the new rational solutions are successfully constructed. Moreover, based on its bilinear formalism, a concise method is employed to explicitly construct its rogue-wave solution and interaction solution with an ansätz function. Finally, the main characteristics

In this paper, we have investigated the Langevin and Brownian equations on fractal time sets using Fα-calculus and shown that the mean square displacement is not varied linearly with time. We have also generalized the classical method of deriving the Fokker–Planck equation in order to obtain the Fokker–Planck equation on fractal time sets.

This paper deals with the mathematical analysis of a general class of epidemiological models with multiple infectious stages for the transmission dynamics of a communicable disease. We provide a theoretical study of the model. We derive the basic reproduction number R0 that determines the extinction and the persistence of the infection. We show that the disease-free equilibrium is globally asymptotically

The kill signals are alert about possible viruses that infect computer network to decrease the danger of virus propagation. In this work, we focus on a fractional-order SEIR-KS model in the sense of Caputo derivative to analyze the effects of kill signal nodes on the virus propagation. For this purpose, we first prove the existence and uniqueness of the model and give qualitative analysis. Then, we