International Journal of Differential Equations

On a Fractional Master Equation

Anitha Thomas

Full-text: Open access

Abstract

A fractional order time-independent form of the wave equation or diffusion equation in two dimensions is obtained from the standard time-independent form of the wave equation or diffusion equation in two-dimensions by replacing the integer order partial derivatives by fractional Riesz-Feller derivative and Caputo derivative of order α,β,1<(α)2 and 1<(β)2 respectively. In this paper, we derive an analytic solution for the fractional time-independent form of the wave equation or diffusion equation in two dimensions in terms of the Mittag-Leffler function. The solutions to the fractional Poisson and the Laplace equations of the same kind are obtained, again represented by means of the Mittag-Leffler function. In all three cases, the solutions are represented also in terms of Fox's H-function.

Article information

Source
Int. J. Differ. Equ., Volume 2011 (2011), Article ID 346298, 13 pages.

Dates
Received: 9 February 2011
Accepted: 25 August 2011
First available in Project Euclid: 25 January 2017

Permanent link to this document
https://projecteuclid.org/euclid.ijde/1485313248

Digital Object Identifier
doi:10.1155/2011/346298

Mathematical Reviews number (MathSciNet)
MR2847597

Zentralblatt MATH identifier
1234.35303

Citation

Thomas, Anitha. On a Fractional Master Equation. Int. J. Differ. Equ. 2011 (2011), Article ID 346298, 13 pages. doi:10.1155/2011/346298. https://projecteuclid.org/euclid.ijde/1485313248


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