Analysis of time-fractional soliton solutions for Kudryashov's law with dual nonlocal nonlinearity and refractive index in optical fibers

Optical solitons in nonlinear fiber optics represent fundamental wave phenomena that maintain their shape during propagation, yet existing analytical methods often fail to capture the complex dynamics of models incorporating dual nonlocal nonlinearity effects. Recent studies have shown significant research gaps in solving Kudryashov's law with simultaneous refractive index variations and multiple nonlinear terms, particularly when conformable derivatives are involved. In this study, we investigate the analytical solutions of Kudryashov's equation with dual nonlocal nonlinearity and refractive index effects in optical fibers using the improved modified Sardar Sub-equation expansion method (IMSSEM). By applying…