On the Solution of Fractional Heat Diffusion

Abstract

When the derivative of a function is non-integer order, e.g. the 1/2 derivative, known as fractional calculus. The fractional heat equation is a generalization of the standard heat equation as it uses an arbitrary derivative order close to 1 for the time derivative. We present a stander solution to an initial-boundary-value - heat equation problem and the solution to an initial-boundary-value -  fractional heat equation problem. Our aim is to apply fractional Laplace trance form method and Fourier trance form method to solve the heat diffusion equations with fractional derivative and integral. In this study we used Fourier and Laplace transform methods. We conclude that the fractional heat equation is a physically legitimate generalization of the standard heat equation that might be used for values α ≈ 1. As expected all solutions sufficiently close to  α satisfy  the boundary conditions and display physically realistic properties