Analytical solution for the time-fractional heat conduction equation in spherical coordinate system by the method of variable separation

Abstract

In this paper, using the fractional Fourier law, we obtain the fractional heat conduction equation with a time-fractional derivative in the spherical coordinate system. The method of variable separation is used to solve the timefractional heat conduction equation. The Caputo fractional derivative of the order 0 < α ≤ 1 is used. The solution is presented in terms of the Mittag-Leffler functions. Numerical results are illustrated graphically for various values of fractional derivative.