Dark-singular, Dark-bright and other optical solitons for conformable resonant nonlinear Schrodinger's equation incorporating Kerr law nonlinearity

In this paper, we studied conformable resonant nonlinear Schrodinger's equation (CRNLSE) incorporating Kerr law nonlinearity. The task is assisted with the help of a couple of robust techniques such as the new extended direct algebraic method and tanh - coth method. The application of these techniques results in a number of novel and interesting solutions such as bright-dark, singular, kink, periodic, and rational solutions alongside their constraint conditions. Moreover, some of the solutions are displayed in 3D and 2D graphs to highlight the physical features of these solutions. The impact of conformable fractional parameters is also studied on the shape dynamics of these solutions through 2D graphs. Proposed solutions show that these methods are effective and powerful for finding traveling wave solutions.