The prevalence of the use of mathematical software has dramatically influenced the evolution of differential equations. The use of these useful tools leads to faster advances in the presentation of numerical and analytical methods. This paper retrieves several soliton solutions to the fractional perturbed Schrödinger’s equation with Kerr and parabolic law nonlinearity, and local conformable derivative. The method used in this article, called the generalized exponential rational function method, also relies heavily on the use of symbolic software such as Maple. The considered model has prominent applications in water optical metamaterials. The method retrieves several exponential, hyperbolic, and trigonometric function solutions to the model. The numerical evolution of the obtained solutions is also exhibited. The resulted wide range of solutions derived from the method proves its effectiveness in solving the model under investigation. It is also recommended to use the technique used in this article to solve similar problems.

数学软件的普及极大地影响了微分方程的发展。这些有用工具的使用导致数值方法和分析方法的呈现更快地发展。本文针对具有Kerr和抛物线法则非线性以及局部适形导数的分数阶摄动Schrödinger方程，检索了几个孤子解。本文中使用的方法，称为广义指数有理函数方法，在很大程度上也依赖于使用符号软件（例如Maple）。所考虑的模型在水光学超材料中具有突出的应用。该方法检索该模型的几个指数，双曲和三角函数解。还显示了获得的解的数值演化。从该方法得出的各种解决方案证明了其在解决所研究模型方面的有效性。还建议使用本文中使用的技术来解决类似的问题。