Similarity Solutions for Multiterm Time-Fractional Diffusion Equation

Abstract

Similarity method is employed to solve multiterm time-fractional diffusion equation. Theorders of the fractional derivatives belong to the interval (0, 1] and are defined in the Caputo sense. We illustrate how the problem is reduced from a multiterm two-variable fractional partial differential equation to a multiterm ordinary fractional differential equation. Power series solution is obtained for the resulting ordinary problem and the convergence of the series solution is discussed. Based on the obtained results, we propose a definition for a multiterm error function with generalized coefficients.