Analysis and numerical computations of the fractional regularized long-wave equation with damping term

This study explores the fractional damped generalized regularized long-wave equation in the sense of Caputo, Atangana-Baleanu, and Caputo-Fabrizio fractional derivatives. With the aid of fixed-point theorem in the Atangana-Baleanu fractional derivative with Mittag-Leffler-type kernel, we show the existence and uniqueness of the solution to the damped generalized regularized long-wave equation. The modified Laplace decomposition method (MLDM) defined in the sense of Caputo, Atangana-Baleanu, and Caputo-Fabrizio (in the Riemann sense) operators is used in securing the approximate-analytical solutions of the nonlinear model. The numerical simulations of the obtained solutions are performed with different suitable values of rho, which is the order of fractional parameter. We have seen the effect of the various parameters and variables on the displacement in figures.

Automated summary

This study examines the existence and uniqueness of solutions to the fractional damped generalized regularized long-wave equation using the fixed-point theorem in the Atangana-Baleanu fractional derivative. The modified Laplace decomposition method is utilized to obtain approximate-analytical solutions for the nonlinear model, while numerical simulations are performed with different values of the fractional parameter to observe the effects of various parameters and variables on displacement.