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Generalized differential transform method for solving a space- and time-fractional diffusion-wave equation. (English) Zbl 1209.35066

Summary: We propose a new generalization of the two-dimensional differential transform method that will extend the application of the method to a diffusion-wave equation with space- and time-fractional derivatives. The new generalization is based on generalized Taylor’s formula and Caputo fractional derivative. Theorems that are never existed before are introduced with their proofs. Several illustrative examples are given to demonstrate the effectiveness of the obtained results. The results reveal that the technique introduced here is very effective and convenient for solving partial differential equations of fractional order.

MSC:

35K57 Reaction-diffusion equations
35L05 Wave equation
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