Nonlinear Schrödinger’s equation and its variation structures assume a significant job in soliton dynamics. The soliton solutions of space-time fractional Fokas–Lenells equation with a relatively new definition of local M-derivative have been recovered by utilizing improved \(\tan (\frac{\phi (\eta )}{2})\)-expansion method and generalized projective Riccati equation method. The obtained solutions are periodic, dark, bright, singular, rational, along with few forms of combo-soliton solutions. These solutions are given under constraints conditions which ensure their existence. The impact of local fractional parameter is featured by its graphical portrayal. 2D and 3D diagrams are drawn to illustrate the efficacy of the conformable fractional order on the behavior of some of those solutions. The secured solutions of this model have dynamic and significant justifications for some real-world physical occurrences. Our study shows that the suggested schemes are effective, reliable, and simple for solving different types of nonlinear differential equations.

非线性薛定ding方程及其变分结构在孤子动力学中起着重要作用。通过使用改进的\（\ tan（\ frac {\ phi（\ eta（））} {2}）\），已经恢复了具有相对较新的局部M导数定义的时空分数Fokas-Lenells方程的孤子解。展开法和广义射影Riccati方程法。所获得的解是周期的，暗的，明亮的，奇异的，有理的，以及几种形式的组合孤子解。这些解决方案是在确保其存在的约束条件下给出的。局部分数参数的影响以其图形描绘为特征。绘制2D和3D图以说明顺应分数阶数对这些解决方案中某些行为的有效性。该模型的安全解决方案对于某些现实世界中的物理事件具有动态且重要的依据。我们的研究表明，所提出的方案对于解决不同类型的非线性微分方程是有效，可靠和简单的。