Fractal fractional analysis of modified KdV equation under three different kernels

Abstract

Fractal fractional (FF) operators have been utilized to simulate many phenomena in several applied sciences and engineering in the last decade. In the literature, the recently presented (2+1) modified KdV (mKdV) equation has not been investigated using FF operators. As a result, a nonlinear mKdV equation is explored in this study using FF operators with various kernels. Under three kernels, we investigate the theoretical and computational aspects of the FF-modified KdV. The suggested equation's computational features are investigated using a hybrid Laplace transform. Graphs and numeric data are used to show the error analysis between the exact and achieved solution. Numeric data and graphics are used to make a comparison of the solution of Caputo, Caputo-Fabrizio (CF), and Atangana-Baleanu (AB) FF mKdV equations. Achieved solutions are depicted through graphs for different fractional orders and fractal dimensions. © 2022