Bifurcation and Sensitivity Analyses With Novel Traveling Wave Solutions in a Stochastic Fractional System for Ion Sound and Langmuir Waves

This paper deals with the system of stochastic fractional equations for the ion sound and Langmuir waves. First, the stochastic fractional‐order governing system is transformed into a planar dynamical system using a traveling wave transformation. Then, bifurcation analysis is carried out based on planar dynamical system theory, and the sensitivity of the system to perturbation strength and frequency is analyzed. In addition, new traveling wave solutions of the governing system are constructed using two distinct methods: the enhanced Kudryashov method and the improved generalized Riccati equation mapping method. These solutions are essential for understanding various complex and intriguing physical phenomena. Finally, the analysis indicates that fractional‐order derivatives and multiplicative noise have a significant impact on the behavior of solutions to the stochastic fractional equations governing ion sound and Langmuir waves.