Application of the Tantawy Technique for Modeling Fractional Ion-Acoustic Waves in Electronegative Plasmas having Cairns Distributed-Electrons, Part (I): Fractional KdV Solitary Waves

Abstract

This work examines both non-fractional and fractional ion-acoustic solitary waves (IASWs) in non-Maxwellian unmagnetized electronegative plasmas (ENPs) consisting of inertial positive and negative ions, as well as inertialess electrons adhering to the Cairns distribution. Our study comprises two primary objectives: the first objective is to utilize the reductive perturbation technique (RPT) to derive an evolutionary wave equation, specifically the quadratic nonlinearity planar Korteweg-de Vries (KdV) equation, which governs the propagation of solitary waves (SWs) in the current model. The secondary objective of this study, which is the core of the subject due to its novelty and importance, is to utilize the “Tantawy technique” for analyzing the fractional planar KdV (FKdV) equation and construct high accuracy and more stable approximations to deeply understand the characteristics of fractional KdV solitary waves (SWs) in the current model. Also, the Laplace new iterative approach (LNIM) is utilized to examine the FKdV equation and derive analytical approximations for the fractional SWs. Subsequently, the results are compared with those produced by the Tantawy technique to assess the effectiveness of each method. Additionally, the absolute error of the generated approximations using the two proposed techniques is quantitatively assessed, followed by comparing these results to evaluate the accuracy, efficiency, stability, fast computations, and low-cost computations of the Tantawy technique relative to the LNIM. The effect of plasma parameters like ion mass ratio, nonthermal, negative ion concentration, and fractional parameters on the characteristics of the KdV–SW profile is numerically investigated. The present investigation could be helpful to in space and astrophysical plasma systems.