Abstract
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.
Highlights
It is complicated to find an analytical solution to many partial differential equations
One of the new definitions presented for local derivatives is conformable derivative
The derivative used in this equation is the conformable fractional derivative
Summary
It is complicated to find an analytical solution to many partial differential equations. Almost all methods of solving differential equations, either numerically or analytically, rely on the use of computer software. Analytical solutions to such equations may not be found. Along with the astonishing advances in computer science and the reinforcement of mathematical software, there have been fundamental changes in analytical methods [1, 3, 4, 7, 10, 11, 18,19,20, 22, 25, 26, 28,29,30, 32, 33].
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