Ion–acoustic waves in a conformable fractional mKdV framework: Solitons, periodic solutions, and Hirota bilinear construction

The main aim of this study is to formulate a space–time fractional modified Korteweg–de Vries (mKdV) model for describing ion-acoustic wave propagation in magnetized, multi-component plasmas. By employing the conformable fractional derivative, we derive a reduced evolution equation and obtain exact traveling wave solutions through three complementary approaches: Integration, Jacobi elliptic constructions, and a Hirota bilinear formulation. These methods yield soliton, kink, and periodic wave families, while the associated phase portraits characterize the corresponding dynamic regimes. The fractional order α systematically modulates the amplitude and width of the solutions, with the classical mKdV limit recovered smoothly as α = 1. The findings provide a physically transparent fractional framework together with analytical benchmark solutions that will be useful for validating numerical solvers and interpreting nonlinear structures in laboratory and space plasmas.