On time-fractional relativistic diffusion equations
Resource
J. Pseudo-Differ. Oper.
Appl. June 2012, Volume 3, Issue 2, pp 229-237, DOI 10.1007/s11868-012-0049-6
Appl. June 2012, Volume 3, Issue 2, pp 229-237, DOI 10.1007/s11868-012-0049-6
Journal
Journal of Pseudo-Differential Operators and Applications
Pages
229-237
Date Issued
2012-06
Date
2012-06
Author(s)
Shieh, Narn-Rueih
Abstract
The purpose of this paper is to consider the Cauchy problem for the time-fractional (both sub- and super-diffusive) relativistic diffusion equation. Based on the viewpoint of theory of pseudo-differential operators, we regard the equation as a pseudo-differential equation, and we act the equation via the space-time transform. The solution is expressed as the convolution of the Green's function (heat kernel) and the initial data. The Green's functions are determined by their Fourier transforms, and are written in terms of Mittag-Leffler functions. © 2012 Springer Basel AG.
Type
journal article
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