Novel doubly periodic and other solutions of the conformable time-fractional (2+1)-dimensional modified KdV-CBS equation

Abstract

In this paper, we aim to derive new explicit expressions for the exact solutions of the time-fractional (2+1)-dimensional modified KdV–Calogero–Bogoyavlenskii–Schiff (mKdV–CBS) equation by employing a modified approach based on Jacobi elliptic functions. This method is particularly powerful and effective, as it yields a wide variety of solutions, including doubly periodic, hyperbolic, and periodic forms. To visualize the behavior and topological structures of these solutions, we utilize Mathematica to generate illustrative surface plots.