On a Fractional Master Equation | Zendy

Anitha Thomas | Zendy

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On a Fractional Master Equation

Author(s) -

Anitha Thomas

Publication year - 2011

Publication title -

international journal of differential equations

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.324

H-Index - 20

eISSN - 1687-9651

pISSN - 1687-9643

DOI - 10.1155/2011/346298

Subject(s) - mathematics , fractional calculus , mittag leffler function , laplace transform , laplace's equation , diffusion equation , mathematical analysis , green's function for the three variable laplace equation , function (biology) , integer (computer science) , wave equation , order (exchange) , integro differential equation , partial differential equation , first order partial differential equation , economy , finance , evolutionary biology , biology , computer science , economics , programming language , service (business)

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-Fellerderivative and Caputo derivative of order ,,1<ℜ()≤2 and 1<ℜ()≤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 -function

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