A new modified conformal expansion method to some nonlinear conformal partial differential equations

In this paper, a new modified conformal expansion method is employed to derive exact solutions to specific nonlinear partial differential equations. Katugampola's derivative and the complex transform are utilized to convert nonlinear partial differential equations into nonlinear ordinary differential equations. The efficacy of the proposed methodology is substantiated through the application to Whitham-Broer-Kaup equations, coupled Burgers equations, and coupled mKdV equations. Various analytical solutions including hyperbolic, singular kink, singular periodic, and trigonometric solutions are extracted. Wave simulations of results found in this paper are also plotted.