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