Finite Difference Approximation of Fractional order Partial Differential Equations

Abstract

In this thesis, we define and investigate the fractional integral. We show fractional derivatives and their relation with fractional partial differential equation. We also present Laplace-Transformation, Mittag-Leffler function and Hilfer derivative operator and show their uses to fractional partial differential equation. We give a numerical solution of one dimensional, and two dimensional fractional order partial differential equations using finite difference methods. We discuss the stability, consistency, convergence and error analysis of the methods used. We give and solve some numerical examples and compare the results obtained with the analytical solutions.