Abstract

We calculate the nonlocal phenomena in optical fibers, which arise from various physical origins, by employing derivatives of arbitrary and non-integer orders (fractional calculus). From the nonlocal Maxwell equations, a fractional Schrödinger equation can be derived. To bridge theoretical developments with practical applications, this study implements the splitting method to spatial derivatives with fractional order to simulate pulse propagation in optical fibers, considering both dispersion and nonlinear effects such as self-phase modulation (SPM). The analysis utilizes a dimensional form of the Schrödinger equation and investigates the impact of the fractional order on the spectral broadening of prechirped Gaussian pulses.