Propagation of dust ion acoustic waves with Riesz fractional derivative

In the research paper, the propagation of nonlinear dust ion acoustic solitary waves in a collisionless dusty plasma consisting of negatively charged dust grains, ions, and isothermal electrons in the background of neutral particles is investigated. The reductive perturbation method has been employed to derive the Korteweg-de Vries (KdV) equation for small but finite-amplitude dust ion acoustic waves. The Agrawal technique is used to convert the regular KdV equation to the space-time fractional KdV equation. The Riemann-Liouville definition of the fractional derivative is used to describe the time fractional operator. The Hirota bilinear method is used to derive the multi-soliton solution of the time fractional KdV equation. The effects of the plasma parameters and time fractional parameters on the multisoliton of dust ion acoustic waves for the system are studied. We have also reported the conversion of two-soliton structures to one soliton, depending on the fractional parameter alpha\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\alpha$$\end{document}. This observation in the plasma literature has never been reported before. The result of the present investigation may be applicable to some plasma environments, such as the Earth's mesosphere, cometary tails, Jupiter's magnetosphere, etc.