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Zbl 1197.34006
Cang, Jie; Tan, Yue; Xu, Hang; Liao, Shi-Jun
Series solutions of non-linear Riccati differential equations with fractional order. (English)
[J] Chaos Solitons Fractals 40, No. 1, 1-9 (2009). ISSN 0960-0779

Summary: Based on the homotopy analysis method (HAM), a new analytic technique is proposed to solve non-linear Riccati differential equation with fractional order. 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 $\hbar/2 \pi$. Besides, it is proved that well-known Adomian's decomposition method is a special case of the homotopy analysis method when $\hbar/2 \pi - 1$. This work illustrates the validity and great potential of the homotopy analysis method for the non-linear differential equations with fractional order. The basic ideas of this approach can be widely employed to solve other strongly non-linear problems in fractional calculus. \par Editorial remark: There are doubts about a proper peer-reviewing procedure of this journal. The editor-in-chief has retired, but, according to a statement of the publisher, articles accepted under his guidance are published without additional control.

MSC 2000:: *34A25 Analytical theory of ODE
34A08
26A33 Fractional derivatives and integrals (real functions)

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Zentralblatt MATH Berlin [Germany]