Abundant families of exact solitary wave solutions for the time-fractional Estevez–Mansfield–Clarkson equation

Abstract

The Estevez–Mansfield–Clarkson (EMC) equation is analytically modified to incorporate conformable time-fractional derivatives. This equation serves as a significant model in mathematical physics, optics, and the study of shape evolution in liquid droplets. In this work, the EMC equation is solved using the Jacobi elliptic function expansion method. Various solitary wave solutions such as dark and bright solitons, and multi-wave solutions are derived in terms of rational, hyperbolic, and trigonometric functions. The physical behavior of these solutions is illustrated graphically through contour plots, as well as 2D and 3D visualizations. To confirm the accuracy of the solutions, numerical simulations are conducted. The study concludes with a discussion of the results and final remarks.