Analytic solution of fractional-order heat- and wave-like equations using generalized n-dimensional differential transform method

Abstract

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. © 2011 Verlag der Zeitschrift für Naturforschung, Tübingen.