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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:
 34A08 Fractional ordinary differential equations 34A25 Analytical theory of ordinary differential equations: series, transformations, transforms, operational calculus, etc. 34A45 Theoretical approximation of solutions to ordinary differential equations
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