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Numerical solutions for systems of fractional differential equations by the decomposition method. (English) Zbl 1063.65055

Summary: We use the Adomian decomposition method to solve systems of nonlinear fractional differential equations and a linear multi-term fractional differential equation by reducing it to a system of fractional equations each of order at most unity. We begin by showing how the decomposition method applies to a class of nonlinear fractional differential equations and give two examples to illustrate the efficiency of the method. Moreover, we show how the method can be applied to a general linear multi-term equation and solve several applied problems.

MSC:

65L05 Numerical methods for initial value problems involving ordinary differential equations
34A34 Nonlinear ordinary differential equations and systems
26A33 Fractional derivatives and integrals
65L60 Finite element, Rayleigh-Ritz, Galerkin and collocation methods for ordinary differential equations
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