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We present both the Lagrangian and Hamiltonian procedures for treatinghigher-order equations of motion for mechanical models by adopting theRiemann-Liouville Fractional integral to describe their action. We point outand discuss its efficacy and difficulties. We also present the physical andgeometric interpretations for the approach we pursue and present the details ofa higher-order harmonic oscillator.

Variational Procedure for Higher-Derivative Mechanical Models in a Fractional Integral Framework