In this work, we are investigating a series of new optical soliton solutions to the perturbed nonlinear Schrödinger equation (PNLSE) having the form of kerr law nonlinearity with conformable space-time fractional. Thereby, two relevant integration tools known as new extended direct algebraic method and extended hyperbolic function method are applied to obtain varieties of optical soliton solutions. The series of soliton solutions with fractional derivative order obtained by these methods can be classified as complex trigonometric and hyperbolic functions as well as other elementary functions. Furthermore, conditions for validity of the obtained analytical solutions, graphical illustration (2-D, 3-D) point out the impact of the fractional-order used.

中文翻译：

---

一系列符合时空分数扰动非线性Schrödinger方程的丰富的新孤子

在这项工作中，我们正在研究一系列扰动的非线性Schrödinger方程（PNLSE）的一系列新的光学孤子解，该方程具有kerr律非线性和适度的时空分数。因此，应用了两个相关的集成工具，称为新的扩展直接代数方法和扩展双曲函数方法，以获得各种光学孤子解。通过这些方法获得的具有分数导数阶的孤子溶液序列可以分类为复杂的三角函数和双曲函数以及其他基本函数。此外，获得的分析解决方案的有效性条件（图形说明（2-D，3-D））指出了所用分数阶的影响。