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We study Lagrangian systems with a finite number of degrees of freedom thatare non-local in time. We obtain an extension of Noether theorem and Noetheridentities to this kind of Lagrangians. A Hamiltonian formalism is then set upfor this systems. $n$-order local Lagrangians can be treated as a particularcase and the standard results for them are recovered. The method is thenapplied to several other cases, namely two examples of non-local oscillatorsand the p-adic particle.

Non-local Lagrangian Mechanics: Noether theorem and Hamiltonian formalism