Series solutions of non-linear Riccati differential equations with fractional order

Jie Cang, Yue Tan, Hang Xu and Shi-Jun Liao

Chaos, Solitons & Fractals, 2009, vol. 40, issue 1, 1-9

Abstract: In this paper, 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 ℏ. Besides, it is proved that well-known Adomian’s decomposition method is a special case of the homotopy analysis method when ℏ=−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.

Date: 2009
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Citations: View citations in EconPapers (9)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:40:y:2009:i:1:p:1-9

DOI: 10.1016/j.chaos.2007.04.018

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