Global Dynamical Analysis, Sensitivity Assessment and Optical Soliton Solutions of the Truncated M-Fractional Stochastic Biswas–Arshed Model

This work investigates the optical soliton solutions and their dynamical behaviors of the fractional stochastic Biswas–Arshed equation (FSBAE). By employing the definition of truncated M-fractional derivative and a wave transformation, we reduce the FSBAE to an integrable ordinary differential equation. Applying the qualitative and bifurcation theory of planar dynamical systems, we analyze its bifurcations and construct five explicit types of exact traveling wave solutions, namely solitary wave solutions, kink-type exponential function solutions, Jacobi elliptic sn-type periodic solutions, Jacobi elliptic cn-type periodic solutions, and exponential-form solitary wave solutions. Furthermore, to explore the model’s sensitivity to perturbations, we introduce a time-periodic perturbation term, then the emergence of chaotic behavior is demonstrated by providing 2D and 3D phase portraits.