Numerical investigation of fractional-order Kersten–Krasil’shchik coupled KdV–mKdV system with Atangana–Baleanu derivative

Abstract In this article, we present a fractional Kersten–Krasil’shchik coupled KdV-mKdV nonlinear model associated with newly introduced Atangana–Baleanu derivative of order which uses Mittag-Leffler function as nonsingular and nonlocal kernel. We investigate the behavior multi-component plasma. For effective approach, named homotopy perturbation, transformation approach is suggested. This scheme generally occurs characterization waves in traffic flow, plasmas, electrodynamics, electromagnetism, shallow water waves, elastic media, etc. The main objective study to provide new class methods, requires not using small variables for finding estimated solution frameworks unrealistic factors eliminate linearization. Analytical simulation represents that suggested method effective, accurate, straightforward use wide range physical frameworks. analysis indicates analytical obtained by perturbation transform very efficient precise evaluation scheme. result also suggests much simpler easier, more convenient than other available mathematical techniques.