Salahshour, SoheilMurad, Muhammad Amin S.Demirbilek, UlviyeMahmood, Salim S.Rezazadeh, Hadi2026-04-212026-04-2120260921-45261873-213510.1016/j.physb.2026.4184392-s2.0-105032375719https://hdl.handle.net/123456789/9077https://doi.org/10.1016/j.physb.2026.418439In this work, we present the optical propagation behavior of Kudryashov's model for arbitrary refractive index and nonlocal nonlinearities within the framework of the conformable derivative, using an effective approach. It aims to solve the prominent problem related to complexity in wave propagation in nonlinear optical media, where conventional solution structures are still not fully understood to represent nonlinear structure of waveforms. We systematically derive several families of exact analytical solutions by using the generalized exponential rational function method (GERFM) and obtain different soliton behavior families with various types of solitons (bright, kink, periodic, singular, and mixed solitons). This approach is able to correctly obtain eight different solution sets with different combinations of hyperbolic and trigonometric functions, which comprehensively proves the strong mathematical background of the proposed model. An exhaustive 2D and 3D graphical representation is provided to illustrate how the propagation of the waves is gradually changed due to different parameters of the conformable derivative and how the fractional order affects the soliton stability and propagation. Finally, from the numerical simulations, we demonstrate that the proposed solution has the ability to adapt to the propagation of the optical pulse even in the non-linear dispersive media with different refractive indexes and non-linear properties. This proposed mathematical model is highly applicable to the fields of optical communications, non-linear photonics, plasma physics, and Quantum Field Theory, since the interaction of waves is essential to all technology fields. The study provides valuable insights to the mathematical physics community through rigorous theoretical analysis based upon which it will be able to solve highly complex nonlinear partial differential equations with conformable derivatives. On the other hand, it provides technical aspects for high-quality optical system of high-level design and to study the wave phenomena in various physical applications.eninfo:eu-repo/semantics/closedAccessNonlinear OpticsArbitrary Refractive IndexOptical SolitonsKudryashov’s ModelNonlocal NonlinearitiesWave PropagationArticle