On two exact solutions of time fractional heat equations using different transforms

Abstract

Two solutions of time fractional differential equations are illustrated. The first one converges to functional space in term of Weyl transform in L2(R), while the second solution approaches to the Fox function with respect to time, by using the Fourier and Laplace-Mellin transforms. The fractional calculus is taken in the sense of the Riemann-Liouville fractional differential operator.