A Note on the Generalized Relativistic Diffusion Equation

Luisa Beghin and Roberto Garra
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Luisa Beghin: Dipartimento di Scienze Statistiche, “Sapienza” Università di Roma, P. le A. Moro 5, 00185 Roma, Italy
Roberto Garra: Dipartimento di Scienze Statistiche, “Sapienza” Università di Roma, P. le A. Moro 5, 00185 Roma, Italy

Mathematics, 2019, vol. 7, issue 11, 1-9

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.

Keywords: relativistic diffusion equation; Caputo fractional derivatives of a function with respect to another function; Bessel-Riesz motion (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2019
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