Hamiltonian Formulation for Continuous Third-order Systems Using Fractional Derivatives

Abstract

We constructed the Hamiltonian formulation of continuous field systems with third order. A combined Riemann–Liouville fractional derivative operator is defined and a fractional variational principle under this definition is established. The fractional Euler equations and the fractional Hamilton equations are obtained from the fractional variational principle. Besides, it is shown that the Hamilton equations of motion are in agreement with the Euler-Lagrange equations for these systems. We have examined one example to illustrate the formalism.

Keywords: Fractional derivatives, Lagrangian formulation, Hamiltonian formulation, Euler-lagrange equations, Third-order lagrangian.