A novel scheme for time‐fractional semi‐relativistic Vlasov–Maxwell system based on laser‐plasma interaction with linear polarization and Landau damping instability

Abstract

AbstractThe Vlasov–Maxwell system is a revolutionary tool to model and analyze the dynamic behavior of the collisionless plasma in the existence of the electromagnetic field. In this perspective, the investigation of this system with the concept of the time‐fractional derivative is the new benchmark and also one of the main objectives of this article. To construct the numerical solution, we propose and implement a novel scheme which grounded on finite‐difference and spectral approximations. The temporal variables are tackled by using finite‐difference approximations, whereas spatial variables approximated via sifted Gegenbauer polynomials. Various simulations are performed to explore new phenomena, demonstrate the accuracy and reliability of the proposed method. Convergence, error bound and stability of the suggested methods are investigated numerically. Moreover, the developed method can be used conveniently to examine the numerical solution of other multidimensional highly nonlinear fractional or variable order problems of physical nature.