Atangana-Baleanu Caputo fractional-order modeling of plasma particles with circular polarization of LASER light: An extended version of Vlasov-Maxwell system

In this study, we design a specific geometry of plasma particles and further translate it into mathematical form, i.e., formulated time-fractional semi relativistic Vlasov Maxwell system. This extended version of model is very significant and ground-breaking because it has ability to study the behavior of plasma particles at macroscopic and microscopic time-evaluation scales, which is not studied yet. This model is further tackled with numerical strategy, projected in accordance with spectral and finite difference approximations. The numerical results demonstrate that there are certain variations of the plasma particles that were out of sight at fractional scale and dynamically, we have entered into the real profundity of the problem. Numerical convergence of the projected technique is also inspected. These designed tools, such as the plasma and numerical methods, are very significant and can say that it is a remarkable contribution in this field. In addition, the established numerical structure can utilize to scrutinize the required numerical solution of highly non-linear and fractional problems.