@article{Alsatami2025, 
author = {Khalid A. Alsatami},
title = {Ion–acoustic waves in a conformable fractional mKdV framework: Solitons, periodic solutions, and Hirota bilinear construction},
year = {2025},
journal = {AIMS Mathematics},
volume = {10},
number = {12},
pages = {29189-29235},
keywords = {partial differential equations, space–time fractional mKdV, ion-acoustic waves, magnetized multi-component plasma, traveling waves, Hirota bilinear method, phase portrait and bifurcation analysis},
url = {https://www.sciopen.com/article/10.3934/math.20251284},
doi = {10.3934/math.20251284},
abstract = {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.}
}