Numerical Methods for Fractional Calculus

Features

• Focuses on numerical techniques for fractional integrals, derivatives, and differential equations
• Covers frequently used fractional integrals and derivatives, including Riemann–Liouville integrals, Riemann–Liouville derivatives, and Caputo derivatives
• Explains how to implement fractional finite difference methods in various fractional differential equations relevant to scientific and engineering applications
• Presents the finite element method for solving FPDEs
• Includes many numerical examples to support the theoretical analyses
• Offers MATLAB code for download on the book’s CRC Press web page

Summary

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® functions are available on the book’s CRC Press web page.