Optimal Solutions of the Time-Fractional Wave Models

In this article, we provide an update on the optimal auxiliary function method (OAFM) in this work. This semi-analytical approach uses the Caputo fractional derivative operator (FOAFM) to solve fractional order differential equations. The efficiency and reliability of the method are shown by using modified equal-width model (MEW), equal-width model (EW), and regularized long wave model (RLW). Hydromagnetics waves in cold plasma are largely dependent on the aforementioned models. Our objective is to study the nonlinear behavior of the plasma system and determine its important features. The results show that even at the first iteration, our proposed method is simple, less expensive computationally, and rapidly converges to accurate results. The presence of the proper auxiliary constants allows for the achievement of convergence and stability. The technique has a remarkable ability to solve many different scientific and technical problems.