Solitons to the time-fractional Radhakrishnan–Kundu–Lakshmanan equation with B and M-truncated fractional derivatives: a comparative analysis

Abstract

In this study, the dynamics of perturbed fractional Radhakrishnan–Kundu–Lakshman (RKL) equation is investigated taking the fractional derivatives as B and M-truncated derivatives. The considered mathematical model is useful in the description of optical pulse propagation through nonlinear fiber optics. A new simple equation method is implemented to construct the exact wave solutions of the fractional RKL equation. The recovered solutions provide bright, singular, and dark solitons along with bright-dark hybrid solitons for this model. The variation in the obtained soliton solutions is observed for increasing value of fractional order of time derivative for B and M-truncated derivatives. The presented results are novel and the proposed technique is applied to examine the considered model for the first time in this work. Because of the significance of the fractional RKL equation in modeling the propagation of solitons through an optical fiber, the recovered solitons are vital for describing and understanding a variety of fundamental physical processes. For more physical illustration and knowledge of the dynamic physical characteristics of this equation, some important solutions have been discussed graphically in the form of 2D and 3D plots by selecting suitable parameters.