Exact soliton solutions of the nonlinear time-fractional Schrödinger equation via Atangana–Baleanu and M-truncated operators

Source abstract

The main objective of this work is to obtain exact soliton solutions for a nonlinear time-fractional equation model describing wave profiles arising in various physical systems. To derive different wave structures associated with the considered model, two analytical techniques are employed: the extended G'\G^2-expansion method and the modified auxiliary equation (MAE) approach. A wave transformation is applied to reduce the nonlinear time-fractional equation to a nonlinear ordinary differential equation (NLODE) by means of the M-truncated and Atangana-Baleanu (AB) fractional operators. Several classes of solutions, including exponential, hyperbolic, and trigonometric wave forms, are obtained. Over and above the analytical results, graphical visualizations of the exact solutions are provided as a means to show the solutions' qualitative behavior. The solutions obtained give a better understanding of the nonlinear time-fractional Schrödinger-type models' analytical structure through the propagation of waves. Our newly obtained solutions profoundly impact the improvement of new theories of fluid dynamics, mathematical physics, soliton dynamics, optical physics, quantum mechanics, and some other physical and natural sciences. To the best of our knowledge, this is the first time that the methods we present are used for the equation we consider. All obtained solutions are verified for validity using the Maple software program.