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Zbl 1185.65140
Zurigat, Mohammad; Momani, Shaher; Odibat, Zaid; Alawneh, Ahmad
The homotopy analysis method for handling systems of fractional differential equations. (English)
[J] Appl. Math. Modelling 34, No. 1, 24-35 (2010). ISSN 0307-904X

Summary: We present an efficient numerical algorithm for solving linear and nonlinear systems of fractional differential equations (FDEs). The homotopy analysis method is applied to construct the numerical solutions. The proposed algorithm avoids the complexity provided by other numerical approaches. The method is applied to solve three systems of FDEs. Results obtained using the scheme presented here agree well with the analytical solutions and the numerical results presented elsewhere. Moreover, an attempt has been made to address few issues like the effect of varying the auxiliary parameter Planck constant over $2\pi$, auxiliary function $H(t)$, and the auxiliary linear operator $\cal L$ on the order of local error and convergence of the method. Also, we show that the homotopy perturbation method and Adomain decomposition method are special cases of the homotopy analysis method.

MSC 2000:: *65L99 Numerical methods for ODE
34A08

Keywords: systems of fractional differential equations; homotopy analysis method; homotopy perturbation method; Adomian decomposition method

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