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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:
65L05Initial value problems for ODE (numerical methods)
34A34Nonlinear ODE and systems, general
26A33Fractional derivatives and integrals (real functions)
65L60Finite elements, Rayleigh-Ritz, Galerkin and collocation methods for ODE