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A reliable algorithm of homotopy analysis method for solving nonlinear fractional differential equations. (English) Zbl 1185.65139
Summary: Based on the homotopy analysis method (HAM), a powerful algorithm is developed for the solution of nonlinear ordinary differential equations of fractional order. The proposed algorithm presents the procedure of constructing the set of base functions and gives the high-order deformation equation in a simple form. Different from all other analytic methods, it provides us with a simple way to adjust and control the convergence region of solution series by introducing an auxiliary parameter \(\hbar\). The analysis is accompanied by numerical examples. The algorithm described in this paper is expected to be further employed to solve similar nonlinear problems in fractional calculus.

MSC:
65L99 Numerical methods for ordinary differential equations
26A33 Fractional derivatives and integrals
34A08 Fractional ordinary differential equations and fractional differential inclusions
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