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Extension and Applications of a Variational Approach with Deformed Derivatives. (arXiv:1706.09504v1 [math-ph])
来源于:arXiv
We have recently presented an extension of the standard variational calculus
to include the presence of deformed derivatives in the Lagrangian of a system
of particles and in the Lagrangian density of field-theoretic models. Classical
Euler-Lagrange equations and the Hamiltonian formalism have been re-assessed in
this approach. Whenever applied to a number of physical systems, the resulting
dynamical equations come out to be the correct ones found in the literature,
specially with mass-dependent and with non-linear equations for classical and
quantum-mechanical systems. In the present contribution, we extend the
variational approach with the intervalar form of deformed derivatives to study
higher-order dissipative systems, with application to concrete situations, such
as an accelerated point charge - this is the problem of the
Abraham-Lorentz-Dirac force - to stochastic dynamics like the Langevin, the
advection-convection-reaction and Fokker-Planck equations, Korteweg-de Vries
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