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Open AccessArticle

A Note on the Generalized Relativistic Diffusion Equation

by Luisa Beghin *,† and Roberto Garra *,†
Dipartimento di Scienze Statistiche, “Sapienza” Università di Roma, P. le A. Moro 5, 00185 Roma, Italy
*
Authors to whom correspondence should be addressed.
These authors contributed equally to this work.
Mathematics 2019, 7(11), 1009; https://doi.org/10.3390/math7111009
Received: 13 September 2019 / Revised: 21 October 2019 / Accepted: 22 October 2019 / Published: 24 October 2019
(This article belongs to the Special Issue Advanced Mathematical Methods: Theory and Applications)
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. View Full-Text
Keywords: relativistic diffusion equation; Caputo fractional derivatives of a function with respect to another function; Bessel-Riesz motion relativistic diffusion equation; Caputo fractional derivatives of a function with respect to another function; Bessel-Riesz motion
MDPI and ACS Style

Beghin, L.; Garra, R. A Note on the Generalized Relativistic Diffusion Equation. Mathematics 2019, 7, 1009.

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