An Efficient Technique to Study Time Fractional Extended Fisher-Kolmogorov Equation

Authors

  • K. Pavani Department of Mathematics, School of Advanced Sciences, Vellore Institute of Technology Vellore-632014, India https://orcid.org/0000-0002-3250-0259
  • K. Raghavendar Department of Mathematics, School of Advanced Sciences, Vellore Institute of Technology Vellore-632014, India https://orcid.org/0000-0001-9582-6662
  • K. Aruna Department of Mathematics, School of Advanced Sciences, Vellore Institute of Technology Vellore-632014, India https://orcid.org/0000-0002-2862-5606

DOI:

https://doi.org/10.37256/cm.5220242433

Keywords:

time-fractional extended Fisher-Kolmogorov equation, natural transform, Adomian decomposition method

Abstract

Reaction-diffusion partial differential equations are among the most widely used equations in applied mathematical modelling. In this study, we examine the solutions of one such equation, namely, the time-fractional extended Fisher-Kolmogorov equation. This equation is widely used in the study of population growth and wave propagation dynamics. The technique we consider is a combination of the natural transform and the Adomian decomposition method. Fractional derivatives are considered with singular and non-singular kernels. The existence and uniqueness of the solutions are presented. We analyse two different cases of the proposed problem to determine the validity and efficacy of the proposed scheme. Additionally, numerical simulation is shown, and the nature of the achieved solution is captured in terms of plots for various fractional orders. The outcome demonstrates that the method is straightforward, efficient, and dependable. The proposed method does not require any predetermined assumptions, linearization, perturbation, or discretization, and it prevents rounding errors. Therefore, the technique is ready to be implemented for a variety of nonlinear time fractional partial differential equations.

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Published

2024-04-08

How to Cite

1.
Pavani K, Raghavendar K, Aruna K. An Efficient Technique to Study Time Fractional Extended Fisher-Kolmogorov Equation. Contemp. Math. [Internet]. 2024 Apr. 8 [cited 2024 May 28];5(2):1200-15. Available from: https://ojs.wiserpub.com/index.php/CM/article/view/2433