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A Note on the Generalized Relativistic Diffusion Equation

Author

Listed:
  • Luisa Beghin

    (Dipartimento di Scienze Statistiche, “Sapienza” Università di Roma, P. le A. Moro 5, 00185 Roma, Italy
    These authors contributed equally to this work.)

  • Roberto Garra

    (Dipartimento di Scienze Statistiche, “Sapienza” Università di Roma, P. le A. Moro 5, 00185 Roma, Italy
    These authors contributed equally to this work.)

Abstract

We study here a generalization of the time-fractional relativistic diffusion equation based on the application of Caputo fractional derivatives of a function with respect to another function. We find the Fourier transform of the fundamental solution and discuss the probabilistic meaning of the results obtained in relation to the time-scaled fractional relativistic stable process. We briefly consider also the application of fractional derivatives of a function with respect to another function in order to generalize fractional Riesz-Bessel equations, suggesting their stochastic meaning.

Suggested Citation

  • Luisa Beghin & Roberto Garra, 2019. "A Note on the Generalized Relativistic Diffusion Equation," Mathematics, MDPI, vol. 7(11), pages 1-9, October.
    • Handle: RePEc:gam:jmathe:v:7:y:2019:i:11:p:1009-:d:279939
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    References listed on IDEAS

    as
    1. A. Kumar & J. Gajda & A. Wyłomańska & R. Połoczański, 2019. "Fractional Brownian Motion Delayed by Tempered and Inverse Tempered Stable Subordinators," Methodology and Computing in Applied Probability, Springer, vol. 21(1), pages 185-202, March.
    2. Anh, V.V. & Leonenko, N.N. & Sikorskii, A., 2017. "Stochastic representation of fractional Bessel-Riesz motion," Chaos, Solitons & Fractals, Elsevier, vol. 102(C), pages 135-139.
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