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Adomian decomposition method for solving fractional nonlinear differential equations. (English) Zbl 1106.65115

Summary: We discuss a new application of the Adomian decomposition method on time fractional nonlinear fractional differential equations. Three models with fractional-time derivative of order \(\alpha\), \(0<\alpha<1\) are considered and solved by means of Adomian decomposition method. The behaviour of Adomian solutions and the effects of different values of \(\alpha\) are investigated. Numerical examples are tested to illustrate the pertinent feature of the proposed algorithm.

MSC:

65R20 Numerical methods for integral equations
26A33 Fractional derivatives and integrals
45K05 Integro-partial differential equations
65M70 Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs
35Q53 KdV equations (Korteweg-de Vries equations)
35K35 Initial-boundary value problems for higher-order parabolic equations
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