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Zbl 1185.65139
Odibat, Zaid; Momani, Shaher; Xu, Hang
A reliable algorithm of homotopy analysis method for solving nonlinear fractional differential equations. (English)
[J] Appl. Math. Modelling 34, No. 3, 593-600 (2010). ISSN 0307-904X

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 2000:: *65L99 Numerical methods for ODE
26A33 Fractional derivatives and integrals (real functions)
34A08

Keywords: fractional differential equation; homotopy analysis method; caputo fractional derivative

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Zentralblatt MATH Berlin [Germany]