Exact Solutions and Dynamical Behavior of the Fractional Pure-Quartic Nonlinear Schrodinger Equation

The fractional pure-quartic nonlinear Schrödinger equation (FPQNLSE) plays an important role in modeling nonlinear wave propagation in complex dispersive media where quartic dispersion dominates the conventional second-order effects.This model has significant applications in nonlinear optics, optical fibers, plasma physics, and other systems with memory and nonlocal properties.In this work, exact analytical solutions of the FPQNLSE with the M-truncated fractional derivative are obtained using the mapping method.Different types of solutions, including elliptic, rational, trigonometric, and hyperbolic forms, are derived.These solutions provide important insights into nonlinear phenomena such as optical pulse propagation, signal transmission, and solitary-wave dynamics.Moreover, MATLAB simulations are presented to illustrate the physical behavior of the obtained solutions and to investigate the influence of the fractional-order parameter on wave propagation.