The conformable space-time fractional perturbed nonlinear Schrödinger equation (PNLSE) having three different laws of nonlinearity namely, Kerr law, parabolic law, and power law is considered in this paper. The PNLSE is a nonlinear model which arises in nano-fibers. An efficient technique called the exp$(-\mathrm{\Phi }(\xi ))$-expansion method is utilized to construct some new soliton solutions of the considered model. As a result, dark, singular, rational and periodic solitary wave solutions are obtained. For the special choice of parameters, the 3D, 2D and contour surfaces of the reported solutions are plotted.

中文翻译：

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具有时空分数导数的纳米纤维中的新孤子解决方案

本文考虑了具有三种不同非线性定律的适形时空分数摄动非线性薛定谔方程（PNLSE），即克尔定律、抛物线定律和幂定律。PNLSE 是在纳米纤维中出现的非线性模型。一种称为 exp 的有效技术$(-\mathrm{\Phi }(\xi ))$-展开方法用于构造所考虑模型的一些新孤子解。结果，得到了暗的、奇异的、有理的和周期性的孤立波解。对于参数的特殊选择，绘制了报告解决方案的 3D、2D 和轮廓表面。