Perturbation of optical solutions and conservation laws in the presence of a dual form of generalized nonlocal nonlinearity and Kudryashov’s refractive index having quadrupled power-law

This paper concentrates on constructing optical soliton solutions for Kudryashov’s law of nonlinear refractive index, stemming from the dual form of nonlocal nonlinearity and the quadrupled-power law. Utilizing the new Kudryashov approach, we derive a range of optical wave patterns for the current model with a conformable fractional derivative. We introduce innovative optical solutions characterized by exponential and hyperbolic functions. These solutions fall into distinct categories, encompassing bell-shaped, bright, singular, and wave optical soliton solutions. To demonstrate the significance of the current optical soliton solutions, we present two-dimensional, three-dimensional, and contour plots for bell-shaped, bright, singular, and wave soliton solutions. Further, we illustrate the behavior of several novel optical solutions through graphical representations for various values of the time parameter and fractional order derivative parameter. It can be asserted that the present method is an efficient technique for investigating optical solutions in various types of Schrödinger equations with fractional and integer orders.