Optical solutions to time-fractional improved (2+1)-dimensional nonlinear Schrödinger equation in optical fibers

In this paper, we investigate the time-fractional improved (2+1)-dimensional nonlinear Schrödinger equation with power-law nonlinearity, group-velocity dispersion, and spatio-temporal dispersion in nonlinear optics. This equation models the propagation of optical pulses in nonlinear optical fibers. We derive novel optical soliton solutions expressed through exponential and hyperbolic functions, which include bright, bell-shaped, wave, and singular solitons. To illustrate the characteristics of these solutions, we provide two-dimensional, three-dimensional, and contour plots that visualize the magnitude of the conformable improved (2+1)-dimensional nonlinear Schrödinger equation. By selecting suitable values for physical parameters, we demonstrate the diversity of soliton structures and their behaviors. Furthermore, we investigated the influence of the temporal parameter and the conformable fractional-order derivative on the behavior of soliton solutions. The results highlighted the effectiveness and versatility of the modified Kudryashov method in addressing both integer- and fractional-order differential equations, providing analytical solutions that deepen our insight into the dynamics of complex optical systems. These results contribute to the advancement of soliton theory in nonlinear optics and mathematical physics.