In this paper, the Saul'yev finite difference scheme for a fully nonlinear partial differential
equation with initial and boundary conditions is analyzed. The main advantage of this …

In this article, developed the compact implicit difference method based Grünwald Letnikov
formula (GLF) to compute the solution of the time-fractional diffusion-wave equation …

Fractional differential equations describe nature adequately because of the symmetry
properties which describe physical and biological processes. In this article, a fourth-order …

Nonlinear fractional differential equations provide suitable models to describe real-world
phenomena and many fractional derivatives are varying with time and space. The present …

The variable-order (VO) fractional calculus can be seen as a natural extension of the
constant-order, which can be utilized in physical and biological applications. In this study …

This paper addresses the numerical study of variable-order fractional differential equation
based on finite-difference method. We utilize the implicit numerical scheme to find out the …

Fractional derivative is nonlocal, which is more suitable to simulate physical phenomena
and provides more accurate models of physical systems such as earthquake vibration and …

The aim of this study is to consider solving an important mathematical model of fractional
order (2+ 1)-dimensional breaking soliton (Calogero) equation by Khater method. The …

In this article, we consider the one-dimensional time-fractional diffusion-wave equation with
fractional order (1<< 2) and introduce a new implicit finite difference scheme. The proposed …

This study, considers the fractional order cable model (FCM) in the sense of Riemann–
Liouville fractional derivatives (R-LFD). We use a modified implicit finite difference …