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Notes on Convergence Results for Parabolic Equations with Riemann–Liouville Derivatives

Author

Listed:
  • Long Le Dinh

    (Division of Applied Mathematics, Thu Dau Mot University, Thu Dau Mot City 75000, Binh Duong Province, Vietnam
    These authors contributed equally to this work.)

  • O’regan Donal

    (School of Mathematical and Statistical Sciences, University of Galway, H91 TK33 Galway, Ireland
    These authors contributed equally to this work.)

Abstract

Fractional diffusion equations have applications in various fields and in this paper we consider a fractional diffusion equation with a Riemann–Liouville derivative. The main objective is to investigate the convergence of solutions of the problem when the fractional order tends to 1 − . Under some suitable conditions on the Cauchy data, we prove the convergence results in a reasonable sense.

Suggested Citation

  • Long Le Dinh & O’regan Donal, 2022. "Notes on Convergence Results for Parabolic Equations with Riemann–Liouville Derivatives," Mathematics, MDPI, vol. 10(21), pages 1-13, October.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:21:p:4026-:d:957871
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    References listed on IDEAS

    as
    1. Changpin Li & Deliang Qian & YangQuan Chen, 2011. "On Riemann-Liouville and Caputo Derivatives," Discrete Dynamics in Nature and Society, Hindawi, vol. 2011, pages 1-15, March.
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