Application of the Tantawy Technique for Modeling Fractional Ion-Acoustic Waves in Electronegative Nonthermal Plasmas, Part (II): Fractional Modified KdV-Solitary Waves

Abstract

Building on our previous analysis of the planar fractional Korteweg-de Vries (FKdV) solitary waves [Part (I)] (El-Tantawy et al., Braz. J. Phys. 55, 123, 2025), this research tackles the more complex realm of fractional modified KdV (mKdV) wave propagation in non-Maxwellian unmagnetized electronegative plasmas (ENPs) composed of inertial positive and negative ions and Cairns-distributed inertialess electrons. Our study has two main objectives: The first one is to derive the cubic nonlinearity mKdV equation, which governs solitary wave (SW) propagation in this plasma model, using the reductive perturbation technique (RPT). The second objective, notable for its novelty and significance, entails utilizing the “Tantawy technique” to analyze the fractional planar mKdV (FmKdV) equation. Thus, highly accurate and stable approximations will be generated to clarify the properties of fractional mKdV solitary waves (SWs) and enable a deeper understanding of the dynamic behavior of these complex phenomena during propagation. Additionally, the Laplace transform iterative method (LTIM) is applied to examine and analyze the FmKdV equation and derive analytical approximations, facilitating a comparative analysis with the results of the Tantawy technique. To evaluate the accuracy of all generated approximations using the two proposed techniques, the absolute error of all generated approximations is estimated compared to the exact solution for the integer case. The influence of various plasma parameters on the characteristic behavior of the profile of the FmKdV-SWs is numerically investigated. This research offers valuable insights into laboratory, space, and astrophysical plasma systems.