Numerical approach for solving time fractional diffusion equation

Abstract

In this article one of the fractional partial differential equations was solved byfinite difference scheme based on five point and three point central spacemethod with discretization in time. We use between the Caputo and theRiemann-Liouville derivative definition and the Grünwald-Letnikov operator forthe fractional calculus. The stability analysis of this scheme is examined by usingvon-Neumann method. A comparison between exact solutions and numericalsolutions is made. Some figures and tables are included.