A Note on an Integral Transformation for the Equivalence between a Fractional and Integer Order Diffusion Model

Abstract

This note tackles the equivalence problem between the fractional and integer order diffusion models. Unlike existing approaches, the existence of a unique integral transformation mapping the solution of the integer order model to a solution of the fractional order model of α=1/2 is proven. Moreover, the corresponding inverse integral transformation is formally established to guarantee the equivalence and well-posedness of the solutions of these models. Finally, as an example, the solution of a fractional order diffusion model α=1/2, obtained through the solution of its integer order counterpart and the proposed transformation, is compared with the solution derived by using the Fourier transform.