Abstract :

This paper presents fractional Euler-Lagrange equations for scalar fields with Yukawa interaction defined in terms of Caputo fractional derivatives. By applying the variational principle to a fractional action S, we obtained the fractional Euler-Lagrange equations of motion. Then we presented Lagrangian and Hamiltonian densities for the fractional scalar fields with interaction of order α. We also provided expressions for fractional Heisenberg equations of motion for scalar fields with Yukawa interaction. Moreover, the classical results are obtained as a particular case of fractional formulation in the limit α→1.