Modeling of phenomena such as anomalous transport via fractional-order differential
equations has been established as an effective alternative to partial differential equations …

This chapter is devoted to time-and space-nonlocal generalizations of the standard Fourier
law, the corresponding generalizations of the classical heat conduction equation and …

This book aims to introduce some new trends and results on the study of the fractional
differential equations, and to provide a good understanding of this field to beginners who are …

In this paper, we consider the numerical resolution of a time-fractional diffusion equation,
which is obtained from the standard diffusion equation by replacing the first-order time …

In this paper, we consider the numerical solution of the time fractional diffusion equation.
Essentially, the time fractional diffusion equation differs from the standard diffusion equation …

The traditional second-order Fokker–Planck equation may not adequately describe the
movement of solute in an aquifer because of large deviation from the dynamics of Brownian …

In this paper, we consider the numerical solution of a fractional partial differential equation
with Riesz space fractional derivatives (FPDE-RSFD) on a finite domain. Two types of FPDE …

The aim of this paper is to develop high-order methods for solving time-fractional partial
differential equations. The proposed high-order method is based on high-order finite …

In this paper, we consider a space–time fractional advection dispersion equation (STFADE)
on a finite domain. The STFADE is obtained from the standard advection dispersion …

In this article, we will discuss the applications of the Spectral element method (SEM) and
Finite element Method (FEM) for fractional calculusThe so-called fractional Spectral element …