## International Journal of Differential Equations

### On a Fractional Master Equation

Anitha Thomas

#### 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 $\alpha ,\beta ,1<\Re (\alpha )\le 2$ and $1<\Re (\beta )\le 2$ 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
Accepted: 25 August 2011
First available in Project Euclid: 25 January 2017

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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