Exploring Optical Soliton Solutions and Bifurcation Analysis in the Space- Time Fractional Fokas-Lenells (STFFL) Equation with Sardar Sub-Equation (SSE) Approach

Abstract The space-time fractional Fokas-Lenells (STFFL) equation is a mathematical model used in telecommunications and transmission technology to describe complex phenomena. It explains nonlinear pulse propagation in optical fibers. In this study, we use the Sardar sub-equation (SSE) approach with the STFFL equation to find unexplored optical soliton solutions (OSSs) and analyze their bifurcations. These OSSs include bright-dark, periodic, multiple bright-dark solitons, and various types. We use 2D, contour, and 3D diagrams to illustrate the impact of fractional and time parameters on these solutions. Additionally, we create 2D, 3D, contour, and bifurcation analysis diagrams to examine the nonlinear effects of the STFFL equation. We establish a Hamiltonian function (HF) for phase plane dynamics analysis and conduct simulations using Python and MAPLE software. The discovered OSS solutions have practical implications for real-world physical events. This study demonstrates the utility and reliability of the SSE scheme for solving time-space nonlinear fractional differential equations (TSNLFDEs).