Similarity solutions of fractional order heat equations with variable coefficients

Abstract

In this work, we use similarity method to solve fractional order heat equations with variable coefficients. The fractional derivative is defined in Caputo sense. Two examples are presented to illustrate how problems are reduced from two-variable partial fractional differential equations to ordinary ones. Series solutions are obtained for the ordinary problems in the form of power series. Based on the obtained results, a definition for an error function with generalized coefficients is proposed in a series form and its convergence is discussed.