Progress in Fractional Differentiation & Applications

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In this article, we developed the Hamiltonian formulation of third-order continuous field systems. A fractional variational principle based on the combined Riemann–Liouville fractional derivative operator is established. The fractional variational principle is used to obtain fractional Euler equations and fractional Hamilton equations. The Hamilton equations of motion are also found to agree with the Euler-Lagrange equations for these systems. Finally, we study an example to elucidate the results.

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