A variety of fractional soliton solutions for three important coupled models arising in mathematical physics

Abstract

This paper deals with the optical solitons of fractional coupled Boussinesq, Burgers-type and mKdV equations by the hypothesis of traveling wave and [Formula: see text]-expansion scheme. These equations are important in different fields such as propagation of long water waves, fluid dynamics, and shallow water wave propagation. In comparison to other analytical procedures, the analytical methodology [Formula: see text] is an incredibly beneficial approach. This technique can also be used with other nonlinear fractional models. The suggested method generates three distinct solutions such as trigonometric, hyperbolic, and rational. Moreover, graphical representation has been used to portray the physical significance of the constructed solutions. Finally, a comprehensive study is made by using a definition of Beta fractional derivative and obtained solutions are represented graphically to understand considered models.