A Fractional-Order Integral Transformation for the Diffusion Model

Resumen: In this paper, the problem of model equivalence between integer-order and fractional-order systems with Caputo derivative is considered. Motivated by diverse studies that show a connection between the diffusion model and its equivalent fractional diffusion models, the construction of the integral transformation is presented that maps the solution of the one-dimensional integer diffusion model to the equivalent solution of the fractional diffusion model. It is demonstrated that the unique integral transformation between both models corresponds to the {integral} of half-order. The derivation includes the inverse integral transformation, which allows the validation of the equivalence and well-posedness of the models. Moreover, the explicit analytic solution for the equivalent fractional partial differential equation is given through the proposed transformation.

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Claudia A. Perez-Pinacho & Cristina Verde. A Fractional-Order Integral Transformation for the Diffusion Model. Memorias del Congreso Nacional de Control Automático, pp. 127-133, 2021.

Palabras clave

Integer-order diffusion model, fractional calculus, integral transformation, fractional-order diffusion model

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