Over the past few decades, there has been substantial interest in evolution equations that
involve a fractional-order derivative of order α∈(0, 1) in time, commonly known as …

The purpose of this book is to present a self-contained and up-to-date survey of numerical
treatment for the so-called time-fractional diffusion model and their mathematical analysis …

This paper is devoted to the construction and analysis of finite difference methods for solving
a class of time-fractional subdiffusion equations. Based on the certain superconvergence at …

This work proposes a new kind of trajectory tracking controller for the differential drive
mobile robot (DDMR), namely, the nonlinear neural network fractional-order proportional …

Starting with an introduction to fractional derivatives and numerical approximations, this
book presents finite difference methods for fractional differential equations, including time …

Based on the weighted and shifted Grünwald operator, a new high-order compact finite
difference scheme is derived for the fractional sub-diffusion equation. It is proved that the …

The fractional reaction-diffusion equation has an important physical and theoretical
meaning, but its analytical solution poses considerable problems. This paper develops an …

In this paper we introduce higher order numerical methods for solving fractional differential
equations. We use two approaches to this problem. The first approach is based on a direct …

In this work, we analyse a Crank-Nicolson type time-stepping scheme for the subdiffusion
equation, which involves a Caputo fractional derivative of order in time. It hybridizes the …

Two difference schemes are derived for both one-dimensional and two-dimensional
distributed-order differential equations. It is proved that the schemes are unconditionally …