Wave dynamics of the conformable fractional high-order Schrödinger equation in inhomogeneous optical fibers

Abstract

This study investigates the conformable fractional high-order nonlinear Schrödinger equation in the context of inhomogeneous optical fibers, a setting where classical models often fall short due to complex dispersion and memory effects. The motivation for selecting this model lies in its capability to capture nonlocal wave behavior more accurately using fractional derivatives. To obtain analytical wave solutions, we apply the Modified Extended Mapping Method (MEMM), which provides a broader and more systematic solution space than conventional techniques. Our findings yield novel families of exact solutions—including bright and dark solitons, exponential, singular, and Jacobi elliptic waveforms. The impact of the fractional-order parameter α on wave structure, velocity, and localization is examined, showing that it significantly modulates soliton behavior without altering peak magnitude. These results highlight both the modeling power of fractional calculus and the utility of MEMM in constructing diverse waveforms, offering potential for improved pulse shaping in advanced optical systems.