  Recently, we have demonstrated that there exists a possible relationship
between q-deformed algebras in two different contexts of Statistical Mechanics,
namely, the Tsallis' framework and the Kaniadakis' scenario, with a local form
of fractional-derivative operators for fractal media, the so-called Hausdorff
derivatives, mapped into a continuous medium with a fractal measure. Here, in
this paper, we present an extension of the traditional calculus of variations
for systems containing deformed-derivatives embedded into the Lagrangian and
the Lagrangian densities for classical and field systems. The results extend
the classical Euler-Lagrange equations and the Hamiltonian formalism. The
resulting dynamical equations seem to be compatible with those found in the
literature, specially with mass-dependent and with nonlinear equations for
systems in classical and quantum mechanics. Examples are presented to
illustrate applications of the formulation. Also, the conserved Nether current,
are worked out.
