A novel method for nonlinear fractional partial differential equations: Combination of DTM and generalized Taylor's formula

Authors:
Shaher Momani;Zaid Odibat
Affiliations:
Department of Mathematics, Mutah University, P.O. Box 7, Al-Karak, Jordan;Prince Abdullah Bin Ghazi Faculty of Science and IT, Al-Balqa' Applied University, Salt, Jordan
Venue:
Journal of Computational and Applied Mathematics
Year:
2008

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Abstract

In this article, a novel numerical method is proposed for nonlinear partial differential equations with space- and time-fractional derivatives. This method is based on the two-dimensional differential transform method (DTM) and generalized Taylor's formula. The fractional derivatives are considered in the Caputo sense. Several illustrative examples are given to demonstrate the effectiveness of the present method. Results obtained using the scheme presented here agree well with the analytical solutions and the numerical results presented elsewhere. Results also show that the numerical scheme is very effective and convenient for solving nonlinear partial differential equations of fractional order.