## 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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