2015/11/09 by José Weberszpil, J. A. Helayël-Neto, José Abdalla Helayël-Neto
Mathematics · Physics and Astronomy · #Applied mathematics #Calculus of variations #Classical mechanics #Dynamical systems theory #Formalism (music) #Fractal #Fractional Differential Equations Solutions #Hamiltonian (control theory) #Hamiltonian mechanics #Lagrangian #Lagrangian system #Mathematical analysis #Mathematical optimization #Mathematics #Noether's theorem #Nonlinear Waves and Solitons #Nonlinear system #Physics #Quantum mechanics #Statistical Mechanics and Entropy #Statistical mechanics #Statistical physics #cond-mat.stat-mech #hep-th #math-ph #math.MP #nlin.SI #quant-ph
paper · pdf · doi:10.1016/j.physa.2015.12.145
published as Phys A 450 (2016) 217-227 · 13 pages. arXiv admin note: text overlap with arXiv:1502.07606
arxiv created 2015/11/09 · openalex publication_date 2016/01/18 · arxiv updated 2016/03/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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.