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.


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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