Pure–Cubic Optical Solitons for the Lakshmanan–Porsezian–Daniel Model with Fractional Temporal Evolution by Riccati’s Method and Kudryashov’s Approach

This paper investigates the propagation of optical solitons governed by the fractional Lakshmanan–Porsezian–Daniel model incorporating cubic–quintic nonlinearities and higher-order perturbation effects. The model captures complex pulse dynamics in nonlinear optical media with memory through a fractional temporal derivative. By employing the addendum Kudryashov method and the unified Riccati equation expansion method, a variety of exact analytical solutions are constructed, including combo, bright, dark, and singular soliton solutions. The obtained solutions reveal the influence of higher-order dispersion, nonlinear perturbations, and fractional dynamics on pulse propagation. The existence conditions for these solitons are derived and discussed. Physically, these solutions are relevant to optical fiber communications, ultrashort pulse propagation, and nonlinear photonic devices, where control over waveform stability and shape is essential. The results contribute to a deeper understanding of nonlinear wave propagation in complex optical systems and may assist in the design of advanced optical transmission technologies.