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arXiv · 1511.02835

Variational Approach and Deformed Derivatives

José Weberszpil·José Abdalla Helayël-Neto
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Abstract

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.

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BibTeXRIS

José Weberszpil, José Abdalla Helayël-Neto. 2015-11-09. Variational Approach and Deformed Derivatives. https://doi.org/10.1016/j.physa.2015.12.145

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