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International Journal of Differential EquationsVolume 2011 2011, Article ID 346298, 13 pages

Research ArticleDepartment of Mathematics, B.A.M. College, Thuruthicadu P.O., Mallapally, Kerala, Pathanamthitta 689597, India

Received 9 February 2011; Accepted 25 August 2011

Academic Editor: Peiguang Wang

Copyright © 2011 Anitha Thomas. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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-Fellerderivative and Caputo derivative of order and 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.





Author: Anitha Thomas

Source: https://www.hindawi.com/



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