Fractional dissipative low-frequency ion-acoustic solitary waves in a nonextensive collisional plasma: An application of the Tantawy technique

This work investigates the linear and nonlinear behavior of low-frequency fractional ion-acoustic waves in a collisional, classical electron-ion plasma using a fluid description. This model consists of inertial ions and inertialess electrons, obeying the nonextensive distribution, with dissipation introduced via ion-neutral collisions. The influence of electron nonextensivity and the ion-neutral collisional parameters on the linear dispersion and damping characteristics of the ion-acoustic waves is analyzed in detail. To explore the nonlinear regime, the governing fluid equations are reduced, via the reductive perturbation technique under the assumption of weak ion-neutral collisionality, to an integer-damped Korteweg-de Vries (KdV) equation. This equation is completely non-integrable and does not admit exact closed-form soliton solutions; thus, the Ansatz method is employed to derive a semi-analytical approximation to investigate the characteristics of dissipative ion-acoustic solitons in the model under consideration. This equation is further generalized to a fractional damped KdV equation by introducing a suitable time-fractional operator, which constitutes the main novelty of the present study. The resulting fractional damped KdV equation is then analyzed analytically using the Tantawy technique, yielding a time-dependent approximate solution that captures the evolution of fractional dissipative ion-acoustic solitons. A comparative numerical analysis is carried out to contrast the dynamics of conventional (integer-order) and fractional dissipative solitons and to quantify the roles of electron nonextensivity and collisionality. The results show that, in the presence of dissipation, the soliton amplitude decays while its width increases with time, and that the nonextensive parameter does not affect the decay rate, which is controlled solely by the dissipative parameter. These findings provide insight into nonlinear wave damping and energy transport in laboratory plasmas and in space environments, such as the ionosphere and the solar wind, where nonextensive electron populations are frequently observed.