Explorating the solition solutions of fractional Chen–Lee–Liu equation with birefringent fibers arising in optics and their sensitive analysis

This study delves into a complex mathematical model, namely the fractional Chen–Lee–Liu (FCLL) model in birefringent fibers which has two components in the form of vector solitons in optical fiber. The FCLL model has remained a uniform fascination for scientists due to its energetic significance in the study of circuit design, signal processing, secure communications, encryption and decryption of chaotic signals, as well as in plasma physics. For the intellectual curiosity of new precise solutions of the selected model, two innovative norms namely, the modified Sardar-sub equation scheme and the improved \({\mathcal {F}}\) $\mathcal{F}$ -expansion method have been suggested in the sense of a M-truncated derivative. By employing the aforementioned strategies the bright, dark, bright-dark, periodic, combo, singular, mixed trigonometric, hyperbolic, exponential as well as rational soliton solutions are segregated. Moreover, we examined the sensitivity analysis of selected model. By selecting appropriate parameters, numerical simulations of the attained outcomes are sketched as interesting figures that present the meaning of the obtained results. The generated outcomes are optimistic, demonstrating that the selected approaches are robust, categorical, and efficient in discovering novel solutions to the variety of complex nonlinear models that have arisen in the recent phase of applied sciences.