Numerical Methods for Fractional Differential Equations

Abstract

AbstractThis chapter presents some typical numerical methods for time and space fractional differential equations. Discretization schemes for the Grünwald–Letnikov, Riemann–Liouville, Caputo, fractal and positive time-fractional derivatives are separately discusse, and validated by easy-to-follow numerical examples. Despite being different from “fractional derivative”, fractal derivatives are still included in this chapter. For the convenience of discussions, we call the equations having fractional derivatives with respect to time/space variable the time/space fractional differential equations (TFDEs/SFDEs for short), respectively. If both time and space fractional derivatives are involved, we call the equations time–space fractional differential equations (TSFDEs).