A fractional approach to Hamiltonian-generalized classical fields : The Hamilton-Jacob technique

We explore classical fields by employing fractional differentials via the fractional Hamilton-Jacobi equation. Specifically, the fractional Hamiltonian equations are established for a particular scenario involving classical fields. This formulation gives rise to equations that bear resemblance to those in classical field theory. In the Hamilton-Jacobi system, we handle an inconsistent Lagrangian comprising variables that represent the scalar field and the fermionic field. To represent the formulas of motion, we construct overall differential formulas with multiple parameters. By considering integrability conditions, we express the system through path integration.