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The symmetric fractional derivative is introduced and its properties are studied. The Euler-Lagrange equations for models depending on sequential derivatives of this type are derived using minimal action principle. The Hamiltonian for such systems is introduced following methods of classical generalized mechanics and the Hamilton's equations are obtained. It is explicitly shown that models of fractional sequential mechanics are nonconservative. The limiting procedure recovers classical generalized mechanics of systems depending on higher order derivatives. The method is applied to fractional deformation of harmonic oscillator and to the case of classical frictional force proportional to velocity.