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.