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

Author

Listed:
  • Claudia A. Pérez-Pinacho

    (Instituto de Ingeniería, Universidad Nacional Autónoma de México, Mexico City 04510, Mexico
    These authors contributed equally to this work.)

  • Cristina Verde

    (Instituto de Ingeniería, Universidad Nacional Autónoma de México, Mexico City 04510, Mexico
    These authors contributed equally to this work.)

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.

Suggested Citation

  • Claudia A. Pérez-Pinacho & Cristina Verde, 2022. "A Note on an Integral Transformation for the Equivalence between a Fractional and Integer Order Diffusion Model," Mathematics, MDPI, vol. 10(5), pages 1-13, February.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:5:p:753-:d:759431
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    References listed on IDEAS

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    2. Metzler, Ralf & Glöckle, Walter G. & Nonnenmacher, Theo F., 1994. "Fractional model equation for anomalous diffusion," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 211(1), pages 13-24.
    3. Jahanshahi, Hadi & Munoz-Pacheco, Jesus M. & Bekiros, Stelios & Alotaibi, Naif D., 2021. "A fractional-order SIRD model with time-dependent memory indexes for encompassing the multi-fractional characteristics of the COVID-19," Chaos, Solitons & Fractals, Elsevier, vol. 143(C).
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