The fractional form of the complex scalar and vector Lagrangian densities is presented using the Caputo’s fractional derivative. Agrawal procedure is employed to obtain equations of motion for both fields in Caputo’s definition. The Hamiltonian density resulting from Lagrangian densities is obtained in fractional form. Then we quantize the Lagrangian density for both standard and vector fields by constructing the fractional creation and annihilation operators and fractional canonical commutation relations (CCRs).

fractional Lagrangian density, fractional canonical quantization, fractional Caputo’s definition.