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

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.