Unveiling the dynamics of fractional optical solitons in cubic–quintic–septimal nonlinear Schrödinger equations

Abstract

This research aims to explore the fractional cubic–quintic–septimal Schrödinger equation. It improves optical signal transmission by controlling dispersion and nonlinear influences. Step-index optical fibers have structured refractive indices. They are frequently used in soliton-based research. Here, two robust integration architectures, the Sardar subequation and the \(G'/(bG'+G+a)\) expansion methods, are implemented to investigate novel soliton solutions with a comparative analysis of the \(\beta -\)fractional and \(M-\)truncated derivatives that expose practical insights into how different fractional definitions affect system dynamics, memory effects, and solution behaviors in complicated models. By utilizing multiple graphical techniques, the study highlights how fractional parameters affect system behavior, memory properties, and soliton formation. The findings hold significant relevance for the mathematical physics community and are especially crucial for advancements in telecommunications.