# A new approach for the generalized Dirac Lagrangian density with Atangana--Baleanu fractional derivative

### Abstract

The Atangana--Baleanu fractional derivative was used to rebuild the Dirac field. This new formulation employs Hamilton's equations, fractional Euler-Lagrange equations, and the Dirac field. We also discover that the equations Euler-Lagrange and Hamilton provide comparable results. The Dirac Lagrangian density is used to compute the Hamilton equations of motion. The fractional Noether's theorem is also used to determine conserved quantities like as energy density, momentum, and Poynting's vector. Only fractional derivatives and integrals of integer orders have the unusual property of containing classical derivatives and integrals as special examples for derivatives of integer orders. As a result, fractional models can only be utilized with classical models. This strategy is useful for explaining complex processes.