Random Fractional Laplace Transform for Solving Random Time-Fractional Heat Equation in an Infinite Medium

Abstract

The random Laplace and Fourier transforms are very important tools to solve random heat problems. Unfortunately, it is difficult to use these random integral transforms for solving the fractional random heat problems, where the mean square conformable fractional derivative is used to express for the time fractional derivative. Therefore, this work adopts the extension of the random Laplace transform into random fractional Laplace transform in order to solve this kind of heat problems. The stochastic process solution of the fractional random heat in an infinite medium is investigated by using  random fractional Laplace transform  together with random Fourier transform. The mean and the standard diffusion of the stochastic process solution is computed for different value of fractional order. When α = 1, the results show  agree with the available results in the references context.