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

Yong Wu (), El-Sayed M. Sherif (), Miguel Vivas-Cortez, Sajjad Ahmad (), Muhammad Shoaib Saleem and Muhammad Umair Shahzad ()
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Yong Wu: General Education Department, Anhui Xinhua University, Hefei, P. R. China
El-Sayed M. Sherif: Mechanical Engineering Department, King Saud University, Al-Riyadh 11421, Saudi Arabia
Miguel Vivas-Cortez: Escuela de Ciencias Físicas y Matemáticas, Facultad de Ciencias Naturales y Exactas, Pontificia Universidad Católica del Ecuador, Sede Quito, Ecuador
Sajjad Ahmad: Department of Mathematics, University of Okara, Okara 56300, Pakistan
Muhammad Shoaib Saleem: Department of Mathematics, University of Okara, Okara 56300, Pakistan5Department of Mathematics University of Okara, Okara 56300, Pakistan, Center for Theoretical Physics Khazar University, Baku, Azerbaijan
Muhammad Umair Shahzad: Department of Mathematics, University of Okara, Western Caspian University, Baku, Azerbaijan

FRACTALS (fractals), 2025, vol. 33, issue 08, 1-23

Abstract: 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.

Keywords: Fractional Derivatives; Fractional Ion Sound and Langmuir Waves; Improved Modified Sardar Sub-Equation Method; Riccati Sub-Equation Method; Nonlinear Partial Differential Equations (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1142/S0218348X25401565

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