Lie Symmetry Analysis and Conservation Laws of the Time-Fractional Relativistic Vlasov-Maxwell Equation in Kinetic Plasma

Abstract

We investigate the time-fractional Vlasov-Maxwell equation, a fundamental model describing the interaction between charged particles and electromagnetic fields in plasma with memory effects captured by fractional time derivatives. Making use of the Lie symmetry method, we classify the symmetry vector fields and construct the one-dimensional optimal system of subalgebras, which in turn yields symmetry reductions and corresponding analytical solutions using variational iteration method(VIM). To complement these reductions, direct multiplier method is applied to derive the whole class of conservation laws associated with the equation. The results provide new insights into the structure of the time-fractional Vlasov-Maxwell equation and demonstrate the effectiveness of symmetry-based techniques in studying nonlinear plasma dynamics with anomalous diffusion.