Homotopy Analysis with Shehu Transform Method for Time-Fractional Modified KdV Equation in Dusty Plasma

In this article, a semi-analytical method for effectively solving the time-fractional modified KdV equation, which describes dust acoustic waves in a non-magnetized dust plasma is presented in the Homotopy Analysis Shehu Transform Method (HASTM). Using the Atangana-Balean time-fractional derivative, a powerful tool is employed to methodically investigate a solution, leveraging the knowledge gathered from its historical predecessors. The HASTM results are essential for enabling simulations, especially when it comes to single waves related to the modified KdV equation. Moreover, the use of fractional derivatives is helpful in gaining a thorough understanding of the inherent nonlinear behavior of this model. This work also provides important insights into the behavior of individual waves in an unmagnetized dust plasma and makes a substantial contribution to our understanding of the system’s complexities at different parameter values. The knowledge obtained from this work contributes to the theoretical systems and has real-world implications for modeling and interpreting intricate wave events in a dusty plasma environment.