Fractional Diffusion with Time-Dependent Diffusion Coefficient

Autor:	Adrián Ricardo Gómez Plata, Felix Silva Costa, E. Capelas de Oliveira
Rok vydání:	2021
Předmět:	Mellin transform Time dependent diffusion Similarity (network science) Integer Fractional diffusion Order (group theory) Applied mathematics Statistical and Nonlinear Physics Diffusion (business) Mathematical Physics Fractional calculus Mathematics
Zdroj:	Reports on Mathematical Physics. 87:59-79
ISSN:	0034-4877
DOI:	10.1016/s0034-4877(21)00011-2
Popis:	In this paper we propose and discuss the fractional diffusion equation with time-dependent diffusion coefficient, considering the Hilfer-type and Weyl fractional derivatives in the time-variable and space-variable, respectively. We apply the similarity method and Mellin transform methodology to find an explicit solution in terms of Fox H-function. We illustrate graphically the diffusive behaviour described by memory and distance effects. We also recover the classical integer order solution as a particular case.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_________::df0d0a7a936bd61daefcdce9b1530ffd https://doi.org/10.1016/s0034-4877(21)00011-2 Zobrazit plný text záznamu Full Text from ScienceDirect