In this paper, we review many recent developments and further applications of nonstandard
finite difference (NSFD) methods encountered in the past decade. In particular, it is a follow …

​​​ Topics in Fractional Differential Equations is devoted to the existence and uniqueness
of solutions for various classes of Darboux problems for hyperbolic differential equations or …

The homotopy perturbation method is a semi-analytical method for solving linear and
nonlinear ordinary/partial differential equations. Since it is extremely difficult to find exact …

In this article, a general formulation for the fractional-order Legendre functions (FLFs) is
constructed to obtain the solution of the fractional-order differential equations. Fractional …

In this article, we study the time‐fractional nonlinear Klein–Gordon equation in Caputo–
Fabrizio's sense and Atangana–Baleanu–Caputo's sense. The modified double Laplace …

In this article, we develop an analytical method for solving fractional order partial differential
equations. Our method is the generalizations of homotopy perturbations Laplace transform …

The foundation of the concepts of fuzzy fractional integral and Caputo gH-partial for fuzzy-
valued multivariable functions is defined. As a result, fuzzy fractional partial differential …

In this paper, we consider a new fractional function based on Legendre and Laguerre
polynomials for solving a class of linear and nonlinear time-space fractional partial …

In this article, optimal control for variable order fractional multi-delay mathematical model for
the co-infection of HIV/AIDS and malaria is presented. This model consists of twelve …

We analytically investigate a nonlinear fractional-order sine-Gordon (sG) equation. The
derivatives considered herein, are taken in Caputo's sense. The Laplace transform together …