Alternative Variational Iteration Elzaki Transform Method for Solving Time‐Fractional Generalized Burgers‐Fisher Equation in Porous Media Flow Modeling

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ABSTRACTIn this paper, we have studied the time‐fractional generalized Burgers‐Fisher equation, which has applications in turbulence modeling, image processing, and biology. A new method called the alternative variational iteration Elzaki transform method (AVIETM) has been used to achieve the results. We employed the proposed method to obtain a solution for the time‐fractional generalized Burgers‐Fisher equation. The convergence and uniqueness of the solutions for the proposed method have been analyzed and discussed. The validity of the AVIETM is shown by numerical simulation and graphs. The method's accuracy have been shown by comparing the results to exact for various values of the fractional order. The obtained results demonstrate that the proposed AVIETM method is straightforward, highly accurate, and efficient.