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Exact solutions of time fractional generalized Burgers–Fisher equation using exp and exponential rational function methods

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Abstract

In this paper, we deployed the Exp Function (EF) and Exponential Rational Function (ERF) methods on the Time Fractional Generalized Burgers–Fisher Equation (TF-GBFE) to investigate its analytical solutions by means of conformable operator. By making use of travelling wave-like transformation on TF-GBFE, the similarity-transformed ordinary differential equation of TF-GBFE reveals the underlying unidirectional kink solutions by means of the Exp function method. More interestingly, the ERF method on TF-GBFE identifies the peakon-like solution and kink solutions. In addition to that we also obtained several particular solutions of TF-GBFE, expressed in terms of hyperbolic and exponential functions. Using 2D and 3D plots, these solutions are graphically illustrated and discussed in a detailed manner.

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Acknowledgements

The authors thank the anonymous referees for their valuable time, effort and extensive comments which help to improve the quality of this manuscript. The authors also thank the Department of Science and Technology-Fund Improvement of S &T Infrastructure in Universities and Higher Educational Institutions Government of India (SR/FST/MSI-107/2015) for carrying out this research work.

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Authors and Affiliations

  1. Department of Mathematics, Srinivasa Ramanujan Centre, SASTRA Deemed to be University, Kumbakonam, Tamil Nadu, 612 001, India

    S. Ramya & K. Krishnakumar

  2. Department of Mathematics, Perunthalaivar Kamarajar Institute of Engineering and Technology, Karaikal, 609 603, India

    R. Ilangovane

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Ramya, S., Krishnakumar, K. & Ilangovane, R. Exact solutions of time fractional generalized Burgers–Fisher equation using exp and exponential rational function methods. Int. J. Dynam. Control 12, 292–302 (2024). https://doi.org/10.1007/s40435-023-01267-6

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  • DOI: https://doi.org/10.1007/s40435-023-01267-6

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