In this paper, a shifted Jacobi-Gauss collocation spectral algorithm is developed for solving numerically systems of high-order linear retarded and advanced differential-difference equations with variable coefficients ...

The principle result of this paper is the following disturbance rejection control scheme for a class of nonlinear dynamical systems. By using the internal model principle, the problem of disturbance damping control is ...

This paper adopts the Adomian decomposition method and the Pade approximation techniques to derive the approximate solutions of a conformable Rosenau-Hyman equation by considering the new definition of the Adomian polynomials. ...

The discrete fractional calculus is used to fractionalize difference equations. Simulations of the fractional logistic map unravel that the chaotic solution is conveniently obtained. Then a Riesz fractional difference is ...

In this article, sufficient conditions for the existence of extremal solutions to nonlinear boundary value problem (BVP) of fractional order differential equations (FDEs) are provided. By using the method of monotone ...

The key aim of the present study is to attain nondifferentiable solutions of extended wave equation by making use of a local fractional derivative describing fractal strings by applying local fractional homotopy perturbation ...

This manuscript aims to investigate a new approach based on the modal series method and eigenvalue decomposition technique to solve a class of nonlinear optimal control problems. For this purpose, a sequence of decoupled ...

The aim of this paper is to study the Cauchy problem of determining a solution of nonlinear elliptic equations with random discrete data. A study showing that this problem is severely ill posed in the sense of Hadamard, ...

This article, presented a shifted Legendre Gauss-Lobatto collocation (SL-GL-C) method which is introduced for solving variable-order fractional Volterra integro-differential equation (VO-FVIDEs) subject to initial or ...

In this paper, the first purpose is to study existence and uniqueness of solutions to a system of implicit fractional differential equations (IFDEs) equipped with antiperiodic boundary conditions (BCs). To obtain the ...