Analytical Study of (2 + 1)-Dimensional Time Fractional Bogoyavlensky-Konopelchenko Model in Plasma and Fluid Dynamics

Abstract

This paper studies the (2 + 1)-dimensional time fractional Bogoyavlensky-Konopelchenko model that is significant in plasma physics and fluid dynamics. We enhance the model with the Caputo fractional derivative to account for memory and hereditary qualities present in complex physical systems. We use a method called the Laplace residual power series approach to find approximate solutions for the governing model. This approach combines the residual power series technique and the Laplace transform to obtain approximate solutions that represent the dynamic behavior of the governing system. Analytical solutions are derived using the proposed approach, and the exact solutions of the system are compared with those explored during the work, and the absolute and relative errors in the classical case are determined. A comparison of the dynamic behavior of the system at different orders of fractional derivatives and the effect of changing order on the behavior of the derived solutions is presented. To connect the numerical results with physical interpretations, physical insights based on the derived solutions are presented by studying the energy evolution in two different cases of initial conditions. This study advances mathematical models for complicated physical processes, paving the way for practical applications in engineering and science.