| Summary: | In this paper, coupled conformable fractional Fokas-Lenells equation with spatio-temporal dispersion is introduced, which is usually used to simulate the propagation model of pulses’ temporal evolution in birefringent fibers. Firstly, the traveling wave transformation is applied to convert the conformable time–space fractional Fokas-Lenells model into two-dimensional planar dynamic system. Secondly, the qualitative analysis of the coupled conformable fractional Fokas-Lenells equation with spatio-temporal dispersion is discussed by using the plane dynamics system. Moreover, two-dimensional phase portraits, three-dimensional phase portraits, Poincaré sections and sensitivity analysis of its perturbed system are drawn by using the Maple mathematical software. Finally, the optical soliton solutions of the coupled conformable fractional Fokas-Lenells equation with spatio-temporal dispersion are obtained by using planar dynamical system method.
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