Overview

Numerical Methods for Fractional Calculus presents numerical methods for fractional integrals and fractional derivatives, finite difference methods for fractional ordinary differential equations (FODEs) and fractional partial differential equations (FPDEs), and finite element methods for FPDEs. The book introduces the basic definitions and properties of fractional integrals and derivatives before covering numerical methods for fractional integrals and derivatives. It then discusses finite difference methods for both FODEs and FPDEs, including the Euler and linear multistep methods. The final chapter shows how to solve FPDEs by using the finite element method. This book provides efficient and reliable numerical methods for solving fractional calculus problems. It offers a primer for readers to further develop cutting-edge research in numerical fractional calculus. MATLAB(R) functions are available on the book's CRC Press web page.

Full Product Details

Author:   Changpin Li ,  Fanhai Zeng
Publisher:   Taylor & Francis Inc
Imprint:   Chapman & Hall/CRC
ISBN:  

9781482253818

ISBN 10:   148225381
Pages:   300
Publication Date:   14 May 2015
Audience:   General/trade ,  College/higher education ,  General ,  Tertiary & Higher Education
Format:   Electronic book text
Publisher's Status:   Active
Availability:   Available To Order  
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Table of Contents

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

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Author Information

Changpin Li is a full professor at Shanghai University. He earned his Ph.D. in computational mathematics from Shanghai University. Dr. Li's main research interests include numerical methods and computations for FPDEs and fractional dynamics. He was awarded the Riemann-Liouville Award for Best FDA Paper (theory) in 2012. He is on the editorial board of several journals, including Fractional Calculus and Applied Analysis, International Journal of Bifurcation and Chaos, and International Journal of Computer Mathematics. Fanhai Zeng is visiting Brown University as a postdoc fellow. He earned his Ph.D. in computational mathematics from Shanghai University. Dr. Zeng's research interests include numerical methods and computations for FPDEs.

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