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Modified homotopy perturbation method: Application to quadratic Riccati differential equation of fractional order

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  • Odibat, Zaid
  • Momani, Shaher

Abstract

In this paper, a modification of He’s homotopy perturbation method is presented. The new modification extends the application of the method to solve nonlinear differential equations of fractional order. In this method, which does not require a small parameter in an equation, a homotopy with an imbedding parameter p∈[0,1] is constructed. The proposed algorithm is applied to the quadratic Riccati differential equation of fractional order. The results reveal that the method is very effective and convenient for solving nonlinear differential equations of fractional order.

Suggested Citation

  • Odibat, Zaid & Momani, Shaher, 2008. "Modified homotopy perturbation method: Application to quadratic Riccati differential equation of fractional order," Chaos, Solitons & Fractals, Elsevier, vol. 36(1), pages 167-174.
    • Handle: RePEc:eee:chsofr:v:36:y:2008:i:1:p:167-174
    DOI: 10.1016/j.chaos.2006.06.041
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    References listed on IDEAS

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    1. He, Ji-Huan, 2005. "Application of homotopy perturbation method to nonlinear wave equations," Chaos, Solitons & Fractals, Elsevier, vol. 26(3), pages 695-700.
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