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

Claudia A. Pérez-Pinacho and Cristina Verde
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Claudia A. Pérez-Pinacho: Instituto de Ingeniería, Universidad Nacional Autónoma de México, Mexico City 04510, Mexico
Cristina Verde: Instituto de Ingeniería, Universidad Nacional Autónoma de México, Mexico City 04510, Mexico

Mathematics, 2022, vol. 10, issue 5, 1-13

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.

Keywords: integer order diffusion model; fractional calculus; integral transformation; fractional order diffusion model (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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