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Series solutions of systems of nonlinear fractional differential equations. (English) Zbl 1187.34007
Summary: Differential equations of fractional order (FDE) appear in many applications in physics, chemistry and engineering. An effective and easy-to-use method for solving such equations is needed. In this paper, series solutions of the FDEs are presented using the homotopy analysis method (HAM). The HAM provides a convenient way of controlling the convergence region and rate of the series solution. It is confirmed that the HAM series solutions contain the Adomian decomposition method solution as special cases.
MSC:
34A08Fractional differential equations
34A25Analytical theory of ODE (series, transformations, transforms, operational calculus, etc.)
34A45Theoretical approximation of solutions of ODE
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