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Zbl 1165.65375
Hosseinnia, S.H.; Ranjbar, A.; Momani, S.
Using an enhanced homotopy perturbation method in fractional differential equations via deforming the linear part. (English)
[J] Comput. Math. Appl. 56, No. 12, 3138-3149 (2008). ISSN 0898-1221

Summary: Convergence and stability are main issues when an asymptotical method like the Homotopy Perturbation Method (HPM) has been used to solve differential equations. In this paper, convergence of the solution of fractional differential equations is maintained. Meanwhile, an effective method is suggested to select the linear part in the HPM to keep the inherent stability of fractional equations. Riccati fractional differential equations as a case study are then solved, using the Enhanced Homotopy Perturbation Method (EHPM). Current results are compared with those derived from the established Adams-Bashforth-Moulton method, in order to verify the accuracy of the EHPM. It is shown that there is excellent agreement between the two sets of results. This finding confirms that the EHPM is powerful and efficient tool for solving nonlinear fractional differential equations.

MSC 2000:: *65L99 Numerical methods for ODE
34A45 Theoretical approximation of solutions of ODE

Keywords: fractional differential equations; homotopy perturbation method; Adams-Bashforth-Moulton method; Riccati equation; asymptotic method; convergence

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Zentralblatt MATH Berlin [Germany]