The primary aim of this work is to investigate the nonlinear fractional Schrödinger equation, which is adopted to describe the ultra-short pulses in optical fibers. A variety of new soliton solutions and periodic solutions are constructed by implementing three efficient mathematical approaches, namely, the improved fractional $F$-expansion method, fractional Bernoulli ($G^{\prime }$/$G)$-expansion method and fractional cosine-sine method. Moreover, the dynamic properties of these obtained solutions are discussed by plotting some 3D and 2D figures. The employed three analytical methods can be widely adopted to solve different types of fractional evolution equations.

中文翻译：

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通过不同分析方法求解非线性分数阶薛定谔方程的新光学孤子

这项工作的主要目的是研究非线性分数阶薛定谔方程，该方程用于描述光纤中的超短脉冲。通过实施三种高效的数学方法，即改进的分数式 $F$ 展开法、分数式伯努利法（ $G^{\prime }$ / $G)$