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Z. Naturforsch. 66a, 581 – 590
(2011)
doi:10.5560/ZNA.2011-0020
Analytic Solution of Fractional-Order Heat- and Wave-Like Equations Using Generalized n-dimensional Differential Transform Method
Department of Applied Mathematics, Institute of Technology, Banaras Hindu University, Varanasi-221005, India
Received February 18, 2011
Reprint requests to: O. P. S.; E-mail:
singhom@gmail.com
In this paper, we have introduced a generalized n-dimensional differential transform method to propose a user friendly algorithm to obtain the closed form analytic solution for n-dimensional fractional heat- and wave-like equations. Three examples are given to establish the simplicity of the algorithm. In Example 5.3, we show that ten terms of the series representing the solution, even in fractional order, give a very accurate solution.
Key words: Generalized n-Dimensional Differential Transform Method; n-Dimensional Fractional Heat- and Wave-Like Equation; Caputo Fractional Derivative.
Mathematics Subject Classification 2000: 35L05; 35C05; 35Q80.