Lie symmetry approach for The Vlasov-Maxwell system of equations

The present paper is intended for the investigation of the fractional integro-differential system called Vlasov-Maxwell system. The method is based on using the geometric vector fields of the symmetries. This system arises for interaction of charged particles in plasma. The fractional derivative is considered in both the Caputo and Riemann-Liouville sense. Under some suitable conditions, we construct the infinitesimal criterion of invariance for detecting Lie symmetries of these equations. In this study, Lie symmetry method for constructing the similarity solutions of the considered system is implemented. The theory is constructed step by step and carefully to apply in the Vlasov-Maxwell system.