Analysis and Comparison of Analytical Methods for Solitary Wave Solutions of the (2+1)-Dimensional Time-Fractional Schrodinger Equation

This study investigates exact traveling-wave solutions of the (2+1)-dimensional time-fractional Schrödinger equation formulated using a generalized conformable derivative. By introducing a suitable traveling-wave transformation, the governing partial differential equation is reduced to a nonlinear ordinary differential equation. Five analytical techniques—the tanh-function method, Exp-function method, modified simple equation method, homogeneous balance method, and ((G’/G))- expansion method—are then applied to construct explicit solution families. The resulting expressions involve hyperbolic, trigonometric, and rational functions, subject to the corresponding parameter restrictions. Selected solutions are visualized using two-dimensional profiles, three-dimensional surface plots, and contour plots to illustrate their behavior for representative parameter values. A comparative assessment of the five techniques is also presented, focusing on their solution structures, auxiliary equations, and algebraic requirements. The findings provide an analytical basis for further investigation of traveling-wave behavior in the considered model. The validity of each solution is assessed through verification against the reduced ordinary differential equation.