Exploring the fractional Hirota Maccari system for its soliton solutions via impressive analytical strategies

Abstract

In the field of marine engineering, the characteristics of wave propagation play an imperative character. In many geographical regions, the key source of environmental effects on artificial floating or stationary structures or seashores is waves. This article deals with the Hirota Maccari system (HMs) via a new fractional derivative operator known as the beta derivative. This aforesaid equation is a significant model which deals with a variety of nonlinear phenomenons in the fields of optical fibers, physics and other scientific fields. A complex wave hypothesis is applied to transform the aforesaid system with beta derivative into an ODE system. The modified Kudryashov’s (New version) and the Auxiliary equation methods are used to build a variety of soliton solutions of HMs with beta derivative. The singular, periodic, bright, dark solitons and mixed solitons are constructed with the above-mentioned approaches via soft computation in Mathematica. Some of them are numerically simulated for 2D and 3D representation. All the solutions of fractional HMs produced by the above two techniques are novel and have not been derived yet.