Novel exact solutions to the fractional PKP equation via mathematical methods

Abstract

In this paper, we have constructed exact solutions of fractional PKP equation by application of the modified Riemann-Liouville fractional derivative of Jumarie through five analytical mathematical methods. The planned fractional PKP model is extensively used in beachfront ocean and coastal engineering to designate the propagation of shallow-water waves. Two-dimensional and three-dimensional representations of the robust structures of a few chosen acquired solutions are provided. Hence, our suggested techniques are simple and effective instruments for creating traveling wave solutions for NLPDEs. Using the computational program Mathematica 13, various solutions are presented in two and three dimensions to illustrate the physical phenomena of these models. This is done by assigning particular values to the constrain parameters. Therefore, our work's inventiveness is demonstrated by the application of many types of new solutions and newly employed creative ways. This facilitates additional research into nonlinear models that realistically capture important physical processes in daily life. For the physical performance, particular results are manipulated by exposing certain values. Hence, scrutinized negotiations have lucrative rewards in nonlinear science. It is vital to perceive that these techniques are genuine, suitable and well-ordered for NLFPDEs.