Approximate analytic solutions of multi-dimensional fractional heat-like models with variable coefficients

Abstract

In this work, the fractional power series method is applied to solve the 2-D and 3-D fractional heat-like models with variable coefficients. The fractional derivatives are described in the Liouville-Caputo sense. The analytical approximate solutions and exact solutions for the 2-D and 3-D fractional heat-like models with variable coefficients are obtained. It is shown that the proposed method provides a very effective, convenient and powerful mathematical tool for solving fractional differential equations in mathematical physics.