A Novel Approximation to the Fractional KdV Equation Using the Tantawy Technique and Modeling Fractional Electron-Acoustic Cnoidal Waves in a Nonthermal Plasma

In this neoteric study, the fractional and non-fractional electron-acoustic (EA) cnoidal waves (CWs) are investigated in an unmagnetized homogeneous non-Maxwellian plasma composed of hot nonthermal electrons following Cairns distribution, cold electrons, and immobile positive ions. To do this, an evolution wave equation (Korteweg-de Vries (KdV) equation) that governs the propagation of these waves in the current model is generated by using the reductive perturbation technique. Analysis of the KdV equation’s nonlinearity coefficient, which dictates the polarity of nonlinear waves that may emerge and propagate in the current model, reveals that this model only supports rarefactive waves. The impact of various plasma parameters, like the nonthermal parameter and the density ratio of hot-to-cold electrons (hot electron concentration), on the essential features of the EACWs is numerically examined. The second objective of this investigation is to explore the fractional-order parameter’s effect on the dynamics of periodic wave propagation within the current model. This is achieved by transforming the non-fractional planar KdV equation into its fractional counterpart and analyzing it using contemporary methods, such as the Tantawy technique, which has proven its efficacy and precision in numerous prior studies.