Exact Solutions to the Nematic Liquid Crystals with Conformable Derivative

The main objective of this work is to construct novel optical soliton solutions for nematic liquid crystals with conformable derivative using the new Kudryashov approach, a method arising in plasma physics and fluid mechanics. The obtained optical soliton solutions such as W-shape, bell shape, singular, dark-bright, bright, dark, and periodic solutions are explored and expressed by the hyperbolic functions, the exponential functions, and the trigonometric functions to clarify the magnitude of the nematic liquid crystals model with conformable derivative. The resulting traveling wave solutions of the equation play an important role in the energy transport in soliton molecules in liquid crystals. This paper contributes to understanding the fantastic features of nematicons in optics and further disciplines. The kinetic behaviors of the real part, imaginary part, and the square of modulus soliton solutions are illustrated by two-dimensional (2D) and three-dimensional (3D) contours graphs choosing the suitable values of physical parameters. It can be noticed that the novel Kudryashov approach is a powerful tool and efficient technique to solve various types of nonlinear differential equations with fractional and integer orders. That will be extensively used to describe many interesting physical phenomena in the areas of gas dynamics, plasma physics, optics, acoustics, fluid dynamics, classical mechanics.