Electromagnetic Interaction into the Lagrangian Density Fermi Field: Fractional Formulation

The fractional form of the electromagnetic interaction into the Lagrangian density Fermi field is introduced using the left-right Riemann-Liouville fractional derivative. Agrawal procedure is employed to obtain Euler-Lagrange equations in the Riemann-Liouville fractional form. Then, the fractional Hamiltonian for these systems is constructed, which is used to find Hamilton's equations of motion in the same manner as those obtained by using the formulation of Euler-Lagrange equations from variational problems. It is found that the classical findings are derived as a special case of the fractional formulation for Euler-Lagrange and Hamiltonian equations in the limit n =1.