INSIGHTS INTO FRACTIONAL ION SOUND AND LANGMUIR WAVES UNVEILED BY ADVANCED ANALYTICAL TECHNIQUES

This work analyzes Langmuir waves and fractional ion sound waves (FISLWs) in the context of space, plasma physics, and fusion control experiments. The soliton solutions have been suggested for controlling such waves, which include bright, periodic, dark-bright, and dark waves using the Riemann–Liouville derivative operator, Riccati Sub-Equation Method (RSM) and Improved Modified Sardar Sub-Equation Method (IMSSEM). These solitons are critical for advancing knowledge of wave-particle interactions through propagation studies, analysis of nonlinear processes, and wave stabilization. With the help of complex 3D and 2D graphics, including contour plots in Mathematica, our approach effectively solves complex nonlinear fractional partial differential equations (PDEs). That is why the outcomes show that our methods are highly efficient for understanding the complex interactions of charged particle ensembles.