Nonlinear space–time fractional KdV model for ion-acoustic shock waves in isothermal-electron, warm-ion plasmas

This paper investigates the nonlinear dynamics of IASW and periodic waves in warm-ion, isothermal-electron plasmas using the stfKdV equation. Exact analytical solutions are obtained through the F-expansion and Hirota’s bilinear approaches, yielding solitary, cnoidal, and multi-soliton waveforms. The effects of the fractional order α and the ion-to-electron temperature ratio σ are systematically analyzed: α regulates the effective dispersive spreading and phase evolution of the waves, while σ controls amplitude and spatial width through its influence on the nonlinear and dispersive coefficients. Phase-portrait and bifurcation analyses reveal the existence of solitary, periodic, and shock-type structures, and demonstrate how fractional-order dispersion alters the topology of the associated dynamical system. The novelties of this work lie in providing a unified analytical and dynamical framework for the stfKdV model and clarifying how α and σ jointly shape soliton morphology and interaction properties. The research enhances the theoretical framework of fractional nonlinear wave models and offers insights applicable to laboratory and space plasmas, as well as other dispersive environments where fractional-order descriptions remain effective.