On Numerical Methods for Fractional Differential Equation on a Semi-infinite Interval

Abstract

Chapter 11 is devoted to numerical solutions of fractional differential equations (FDEs) on a semi-infinite interval. This chapter presents a broad discussion of spectral techniques based on operational matrices of fractional derivatives and integration methods for solving several kinds of linear and nonlinear FDEs. We present the operational matrices of fractional derivatives and integrals for some orthogonal polynomials/functions on a semi-infinite interval, and use them together with different spectral techniques for solving the aforementioned equations on a semi-infinite interval. Numerous examples are presented to illustrate the numerical and theoretical properties of various spectral techniques for solving FDEs on a semi-infinite interval.