Generalized fractional diffusion equation with arbitrary time varying diffusivity

Ashraf M. Tawfik and Hamdi M. Abdelhamid

Applied Mathematics and Computation, 2021, vol. 410, issue C

Abstract: Anomalous diffusion processes in many complex systems are frequently described by the diffusion equation with a time-dependent diffusion coefficient. This paper introduces an exact solution to the broad classes of the fractional diffusion equation with the arbitrary time-dependent diffusion coefficient by using the Laplace-Fourier technique. The Riesz fractional derivative serves to replace the Laplacian operator, while the new regularized Caputo-type fractional derivative is employed instead of the time derivative. We examine our results by introducing and analyzing the most three common cases that represent diffusivity that varying with time. Our calculation shows exact matching with the probability distribution function and mean square displacement illustrated in the literature.

Keywords: Fractional calculus- Anomalous diffusion- Fox’s H-function (search for similar items in EconPapers)
Date: 2021
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0096300321005385
Full text for ScienceDirect subscribers only

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:410:y:2021:i:c:s0096300321005385

DOI: 10.1016/j.amc.2021.126449

Access Statistics for this article

Applied Mathematics and Computation is currently edited by Theodore Simos

More articles in Applied Mathematics and Computation from Elsevier
Bibliographic data for series maintained by Catherine Liu ().