Dynamical Study of Time Fractional Non-Linear Wave-Like and Fisher’s Equations Using Approximate Technique

Authors

  • Hafiz Muhammad Younas RIPHAH International University Faisalabad.
  • Waqas Nadeem RIPHAH International University Faisalabad
  • Romasa Shafiq RIPHAH International University Faisalabad

Keywords:

Fisher’s Equation, Wave-Like Equation, Initial Condition, Approximate Solution, Approximate Technique. Fractional Calculus.

Abstract

The Homotopy Perturbation Method (HPM) is a powerful and dynamic technique for solving both linear and nonlinear partial differential equations. Since obtaining an exact solution for a nonlinear partial differential equation is challenging, perturbation approaches become valuable based on their criteria. The Homotopy Perturbation Method offers an approximate solution by utilizing the given conditions. It is worth noting that only a few terms are needed to achieve a highly accurate approximate solution. In this paper, we have employed this method and obtained the most accurate result by considering only four terms. The graphical representation of the result illustrates the precise physical situation and the accuracy of the solution. The HPM enables us to find the solution of nonlinear fractional order partial differential equations in the form of a series with easily computable components. Through the calculations and graphical representation, it becomes evident how the solution of the original equation and its behavior depends on the initial conditions.

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Published

2023-12-15