On a Fractional Master Equation. (30th October 2011)

• Record Type: Journal Article
• Authors: Thomas, Anitha
• Other Names: Wang Peiguang Academic Editor.
• Is Part Of: International journal of differential equations. Volume 2011(2011)
• Publication Date: 2011-10-30
• Subjects: Differential equations -- Periodicals; Differential equations; Periodicals; 515.35
• DOI: 10.1155/2011/346298
• Languages: English
• ISSNs: 1687-9643

Abstract

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 orderα, β, 1 < ℜ ( α ) ≤ 2 and1 < ℜ ( 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'sH -function.