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.

提出了一种利用修正的Riemann-Liouville分数阶导数规则和两种带有Mittag-Leffler函数的分数双函数方法的新策略来求解分数非线性模型。例如，该策略解决了时空分数Fokas-Lenells方程，发现了一些新的精确解析解，包括亮孤子，暗孤子，组合孤子和周期解。还对两种分数对偶函数方法进行了比较。这些解决方案在非线性弥散，非线性和自加扰动参数之间存在约束。为了进一步研究光孤子的传输并更好地了解模型背后的物理现象，提供了分数阶孤子解的动力学特性，包括一些图形和分析。研究了分数阶参数的作用。