Propagation of solitary and periodic waves to conformable ion sound and Langmuir waves dynamical system

This article pays attention to secure the exact wave structures to the system of ion sound under influence of ponderomotive force. It is caused by non-linear force and is experienced by a charged particle in an oscillating electromagnetic field of inhomogeneity. The studied equation is analyzed by the assistance of conformable time-fractional and composed of normalized density perturbation and normalized electric field of the Langmuir oscillation. The solutions are extracted with the assistance of new extended direct algebraic method, a relatively new integration tool. We extract various wave structure in solitons in different forms like, bright, dark, combo, and singular soliton solutions. In addition to being helpful for elucidating FNLPDEs, the technique both returns solutions that have already been retrieved and generates new exact solutions. Assuming appropriate parameter values, a variety of graph shapes are sketched to describe the graphical presentation of the calculated outcomes. We anticipate that many engineers who use engineering models will find this study to be of interest. The results demonstrate the viability, ease of use, and scalability of the selected computational approach, even when applied to complex systems.