Dynamical characteristics and modulation instability (MI) analysis of sharp slope bell soliton and kink wave solutions to the perturbed space-time fractional Boussinesq equation

To attain soliton results for the nonlinear fractional progression equations (NLFEEs) like the space-time fractional Boussinesq equation, we have utilized the advanced expansion technique. In this study, solutions are explicitly determined as kink, soliton, and sharp slope ‎bell soliton types. These obtained singular wave solutions might play a significant role in finding the mathematical model of the realistic corporal phenomena. The results illustrated that the advanced- expansion technique is a simple, straightforward, and actual mathematical ‎model for searching extensive wave solutions with suitable parameters of higher-dimensional NLFEEs. We have also applied the modulation instability analysis (MI) to deliberate the consistency scrutiny of the achieved solutions, and the driving character of the obtained waves is ‎inspected, which ensures that all achieved solutions are explicit, reliable, exact, and stable‎.