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On the Solutions of Fractional Burgers-Fisher and Generalized Fisher’s Equations Using Two Reliable Methods

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  • A. K. Gupta
  • S. Saha Ray

Abstract

Two reliable techniques, Haar wavelet method and optimal homotopy asymptotic method (OHAM), are presented. Haar wavelet method is an efficient numerical method for the numerical solution of arbitrary order partial differential equations like Burgers-Fisher and generalized Fisher equations. The approximate solutions thus obtained for the fractional Burgers-Fisher and generalized Fisher equations are compared with the optimal homotopy asymptotic method as well as with the exact solutions. Comparison between the obtained solutions with the exact solutions exhibits that both the featured methods are effective and efficient in solving nonlinear problems. The obtained results justify the applicability of the proposed methods for fractional order Burgers-Fisher and generalized Fisher’s equations.

Suggested Citation

  • A. K. Gupta & S. Saha Ray, 2014. "On the Solutions of Fractional Burgers-Fisher and Generalized Fisher’s Equations Using Two Reliable Methods," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2014, pages 1-16, May.
    • Handle: RePEc:hin:jijmms:682910
    DOI: 10.1155/2014/682910
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    Cited by:

    1. Majeed A. Yousif & Faraidun K. Hamasalh, 2023. "A Hybrid Non-Polynomial Spline Method and Conformable Fractional Continuity Equation," Mathematics, MDPI, vol. 11(17), pages 1-18, September.
    2. Yousif, Majeed A. & Hamasalh, Faraidun K., 2024. "The fractional non-polynomial spline method: Precision and modeling improvements," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 218(C), pages 512-525.

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