Study the behavior of soliton solution, modulation instability and sensitive analysis to fractional nonlinear Schrödinger model with Kerr Law nonlinearity

The Fractional Nonlinear Schrodinger Model (FNLSM) with Kerr law nonlinearity, a popular model for simulating a variety of physical events, is the subject of this study. Our research has two main goals. First, we want to identify novel soliton solutions for the FNLSM with Kerr law nonlinearity, including bright, single, exponential, periodic, hyperbolic, dark and combinations thereof. We use a modified Sardar sub-equation technique to achieve these solutions, which have not yet been published. Secondly, demonstrate that the model is stable and sensitive, examine its modulation instability and sensitivity analysis. To validate the physical relevance of our results, we present 2D, 3D and contour plots with appropriate parameter values. Our results indicate that this research's methodology is effective computationally faster and provides comprehensive and standard solutions. In engineering, computational physics and fiber optics, it can be helpful in resolving more complicated occurrences. By offering novel approaches to currently studied features of FNLSM, this paper advances computational physics. The results that have been presented illustrate the potential for our method to fundamentally alter how FNLSM is understood and modeled. In this dynamic field, we believe that our research offers novel opportunities for investigation and advancement. To the best of our knowledge, this study represents a unique approach to investigating the FNLSM with Kerr law nonlinearity.