Fractional differential transform method combined with the Adomian polynomials

Fractional differential transform method combined with the Adomian polynomials

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Article ID: iaor20121901
Volume: 218
Issue: 12
Start Page Number: 6899
End Page Number: 6911
Publication Date: Feb 2012
Journal: Applied Mathematics and Computation
Authors:
Keywords: programming: nonlinear
Abstract:

A modification of the fractional differential transform method (FDTM) for solving nonlinear fractional differential equations (FDEs) is presented. In this technique, the nonlinear term is replaced by its Adomian polynomial of index k. Then the dependent variable components are replaced in the recurrence relation by their corresponding differential transform components of the same index. Thus nonlinear FDEs can be easily solved with less computational work for any analytic nonlinearity due to the properties and available algorithms of the Adomian polynomials. Numerical examples with different types of nonlinearities are solved and good results are obtained.

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