Analytic Solutions of Fractional Zoomeron Equation Via Power Index Approach and Stability Analysis of Traveling Wave Transformation

The aim of this paper is to study the stability analysis and closed- form solutions of conformable time-fractional Zoomeron equation in porous media. By utilizing function transformation and adjusting indexes of the transformation via Power Index Method (PIM), we can reduce the partial differential equation to ordinary differential equation. The exact solutions of the ordi- nary differential equation can be obtained by using symbolic package Maple. Our finding are more general and contain fractional derivative parameter. The study shows that the used method is effective and reliable. We apply the con- formable derivative and illustrated the application of Zoomeron equation in fractal porous media with traveling wave transformation. We have obtained the trajectory of Zoomeron equation by using eigenvalues and eigenvectors of Jacobian matrices at a fixed points.