Abstract
With the historical review, it can determine that plasma scientists devolved many numerical schemes in literature to solve the kinetic plasma models such as Vlasov- Maxwell system, but the fatal problem is that most of the designed algorithms violate the conservation laws. This issue is significant and cannot disregard because the Vlasov Maxwell system is connected with conservations properties and can evaluate after performing some effective mathematical operations. In this prospective, we formulated the Atangana-Baleanu fractional derivative with Caputo concepts based fractional-order plasma model to study the fractional performance of the plasma particles and further suggested a higher-order conservative numerical algorithm that follows the conservation laws, based on operational matrices theory which is evaluated by using the concepts of Shifted Gegenbauer estimations. The numerical convergence of the designed algorithm is also inspected to validate the competency and compatibility. The comprehensive analysis of the fractional performance of the plasma particles is also part of the study. Moreover, this concept can extend to the variable order and multi-dimensional problems for Vlasov and Boltzmann system. (C) 2021 THE AUTHORS. Published by Elsevier BV on behalf of Faculty of Engineering, Alexandria University.