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Solutions of the initial value problem for nonlinear fractional ordinary differential equations by the rach-Adomian-meyers modified decomposition method. (English) Zbl 1245.65087
Summary: We present the generalized Adomian-Rach theorem and the generalized Rach-Adomian-Meyers modified decomposition method for solving multi-order nonlinear fractional ordinary differential equations. We consider different classes of initial value problems for nonlinear fractional ordinary differential equations, including the case of real-valued orders and another case of rational-valued orders, which are solved by the present method. This method can treat any analytic nonlinearity. The coefficients of the solution in the form of a generalized power series are determined by a convenient recurrence scheme, which does not involve integration operations compared with the classic Adomian decomposition method.
65L05Initial value problems for ODE (numerical methods)
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