Dynamical characteristic of analytical fractional solitons for the space-time fractional Fokas-Lenells equation

A new strategy exploiting together the modified Riemann–Liouville fractional derivative rule and two kinds of fractional dual-function methods with the Mittag–Leffler function is presented to solve fractional nonlinear models. As an example, the space-time fractional Fokas-Lenells equation is solved by this strategy, some new exact analytical solutions including bright soliton, dark soliton, combined soliton and periodic solutions are found. The comparison of two kinds of fractional dual-function methods is also presented. These solutions exist under a constraint among parameters of nonlinear dispersion, nonlinearity and self-steepening perturbation. In order to further study the optical soliton transport and better understand the physical phenomenon behind the model, dynamical characteristics of analytical fractional soliton solutions including some graphics and analysis is provided. The role of the fractional-order parameter is studied.

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