A study of the fuzzy fractional Burger-Huxley, Huxley and Burger equation arising in the different branches of engineering using a novel technique

This article emphasized finding the approximate analytical solution of the fuzzy fractional nonlinear Burger-Huxley, Huxley, and Burger equation using the Homotopy Analysis Elzaki Transform Method (HAETM). The most attractive part of this article is that we have used fuzzy initial conditions with the Fuzzy Fractional Differential Equation (FFDE) defined in the Caputo derivative sense. This is the first time that the Burger-Huxley, Huxley, and Burger equations are solved in a fuzzy environment. As a result, we get two approximate solutions, namely upper and lower bound approximate solutions of the Burger-Huxley, Huxley, and Burger equation. We have shown the uniqueness of the solution obtained using the proposed method. A convergence theorem is established for the HAETM. For the rapid convergence of the series solutions, the nonlinear term present in the equation is expanded as a homotopy polynomial. A comparison of the exact solution with the results obtained by the proposed method. A numerical comparative analysis is done between the Elzaki Homotopy Transformation Perturbation Method (EHTPM) and our proposed method, HAETM, which shows the accuracy of the obtained results by HAETM. Different graphical representations and numerical computational values justify that the proposed method is very effective, efficient, and simple in solving various fuzzy FDEs arising in the different branches of science and technology. The primary purpose of this article is to solve the fractional Burger-Huxley, Huxley, and Burger equations in a fuzzy environment to get generalized approximate solutions and develop some theoretical analysis, graphical presentation, tabular values, and comparative analysis between methods to check the effectiveness of the technique HAETM.

کلیدواژه ها:

Fuzzy fractional ، Burger-Huxley ، Huxley and Burger equation ، Homotopy analysis Elzaki transform method ، Convergence analysis ، upper and lower bound fuzzy solution ، Caputo fractional derivative