Ion Acoustic Solitary Wave Solutions in the Context of the Nonlinear Fractional KdV Equation

Mona Elmahi
Department of Mathematics
College of Science
 Qassim University
 Buraydah, 51452, Saudi Arabia

Nidal.E.Taha
Department of Mathematics
College of Science
 Qassim University
 Buraydah, 51452, Saudi Arabia

Agaeb Mahal Alanzi
Department of Mathematics
College of Science
 Qassim University
 Buraydah, 51452, Saudi Arabia

Manahil Alamin M. Ashmaig
Department of Mathematics
College of Science
 Qassim University
 Buraydah, 51452, Saudi Arabia

Dr. Manal Yagoub Ahmed Juma
Department of Mathematics
College of Science
 Qassim University
 Buraydah, 51452, Saudi Arabia
عنوان البريد الإلكتروني هذا محمي من روبوتات السبام. يجب عليك تفعيل الجافاسكربت لرؤيته.

Keywords: KdV model, fractional calculus, quantum plasma, solitary waves, ion acoustic

Abstract
 This manuscript provides a comprehensive investigation of the fractional (1+1)-dimensional nonlinear Korteweg-de Vries (KdV) model in the context of quantum plasma. The primary objective is to derive and mathematically explain the fractional (1+1)-dimensional nonlinear KdV model within quantum plasmas, focusing on ion acoustic solitary waves. Using the reductive perturbation technique, the fractional KdV equation is formulated and solved via the tanh hyperbolic function technique. The study examines the effects of ion pressure and an external electric field on ion acoustic waves, considering plasma characteristics such as ion-electron temperature ratios, nonextensive electron and positron effects. The manuscript investigates the influence of the fractional order and plasma parameters on the phase velocity of ion acoustic waves. Notably, the results reduce to known outcomes when the fractional order equals one. This work contributes significantly to the understanding of nonlinear phenomena in quantum plasmas, particularly ion acoustic waves, with potential applications in astrophysical and cosmological contexts