In this review paper, we are mainly concerned with the numerical methods for solving
fractional equations, which are divided into the fractional differential equations (FDEs), time …

In this article, our purpose is to study the existence and uniqueness of a solution to a
damped variable order fractional subdiffusion equation with time delay. Under weak …

This paper investigates a class of the time-fractional diffusion-wave equation (TFDWE),
which incorporates a fractional derivative in the Caputo sense of order α+ 1 where 0< α< 1 …

The main purpose of the current paper is to propose a new numerical scheme based on the
spectral element procedure for simulating the neutral delay distributed‐order fractional …

In this paper, we construct and analyze a linearized finite difference/Galerkin–Legendre
spectral scheme for the nonlinear Riesz-space and Caputo-time fractional reaction–diffusion …

This paper is concerned with numerical solutions of nonlinear time fractional reaction–
diffusion equations with time delay. A linearized compact finite difference scheme is …

The delay PDEs are called partial functional differential equations as their unknown
solutions are used in these equations as functional arguments. On the other hand, a neutral …

A delay PDE is different from a PDE in which it depends not only on the solution at a present
stage but also on the solution at some past stage (s). In the current paper, we develop …

In this paper, compact finite difference schemes with (3-α)-th order accuracy in time and
fourth order accuracy in space based on the L 1 method are constructed for time-fractional …

This paper investigates a nonlinear time-fractional mixed sub-diffusion and diffusion-wave
equation with delay. The problem is particularly challenging due to its nonlinear nature, the …