An Innovative Approach to Nonlinear Fractional Shock Wave Equations Using Two Numerical Methods

In this research, we propose a combined approach to solving nonlinear fractional shock wave equations using an Elzaki transform, the homotopy perturbation method, and Adomian decomposition method. The equation is first transformed into equivalent integral transform. method are then utilized approximate solution of equation. To evaluate effectiveness proposed conduct several numerical experiments compare results with existing methods. show that provides accurate efficient solutions for equations. Overall, research contributes development powerful tool equations, which has potential applications in many fields science engineering. This study presents combination transform employed demonstrated through examples compared other