Numerical Methods for Fractional Calculus

Introduction to Fractional Calculus
Fractional Integrals and Derivatives
Some Other Properties of Fractional Derivatives
Some Other Fractional Derivatives and Extensions
Physical Meanings
Fractional Initial and Boundary Problems

Numerical Methods for Fractional Integral and Derivatives
Approximations to Fractional Integrals
Approximations to Riemann–Liouville Derivatives
Approximations to Caputo Derivatives
Approximation to Riesz Derivatives
Matrix Approach
Short Memory Principle
Other Approaches

Numerical Methods for Fractional Ordinary Differential Equations
Introduction
Direct Methods
Integration Methods
Fractional Linear Multistep Methods

Finite Difference Methods for Fractional Partial Differential Equations
Introduction
One-Dimensional Time-Fractional Equations
One-Dimensional Space-Fractional Differential Equations
One-Dimensional Time-Space Fractional Differential Equations
Fractional Differential Equations in Two Space Dimensions

Galerkin Finite Element Methods for Fractional Partial Differential Equations
Mathematical Preliminaries
Galerkin FEM for Stationary Fractional Advection Dispersion Equation
Galerkin FEM for Space-Fractional Diffusion Equation
Galerkin FEM for Time-Fractional Differential Equations
Galerkin FEM for Time-Space Fractional Differential Equations

Bibliography

Index