In this paper, we investigate the (2+1)-dimensional complex modified Korteweg-de Vries (CmKdV) system using the conformable derivative. The CmKdV system is a beneficial model in the field of nonlinear wave theory such as fluid flow, optical communication, and plasma physics. Explicit solutions are constructed, including periodic, solitary, and shock waves form using the Jacobi elliptic function expansion method. The solutions obtained are visually presented in various dimensions using Mathematica, providing a clear physical understanding of the effects of the conformable fractional derivative. This research enhances understanding of soliton behavior in complex nonlinear systems and demonstrates the effectiveness of combining conformable derivatives with analytical methods, while also providing new insights into the dynamics and diverse forms of propagating fluid waves.
Khan et al. (Fri,) studied this question.