Fractional Caputo Heat Equation Within the Double Laplace Transform

Abstract

The heat equation and its fractional generalization are used in various applications in science and engineering. In this paper firstly we introduce the double Laplace transform of the partial fractional integrals and derivatives which can be used to solve partial differential equations with Caputo fractional derivatives. Secondly, the fractional heat equation was investigated in details with the help of this new generalized transform