36,281 research outputs found
Towards a combined fractional mechanics and quantization
A fractional Hamiltonian formalism is introduced for the recent combined
fractional calculus of variations. The Hamilton-Jacobi partial differential
equation is generalized to be applicable for systems containing combined Caputo
fractional derivatives. The obtained results provide tools to carry out the
quantization of nonconservative problems through combined fractional canonical
equations of Hamilton type.Comment: This is a preprint of a paper whose final and definite form will be
published in: Fract. Calc. Appl. Anal., Vol. 15, No 3 (2012). Submitted
21-Feb-2012; revised 29-May-2012; accepted 03-June-201
Macroscopic description of microscopically strongly inhomogenous systems: A mathematical basis for the synthesis of higher gradients metamaterials
We consider the time evolution of a one dimensional -gradient continuum.
Our aim is to construct and analyze discrete approximations in terms of
physically realizable mechanical systems, called microscopic because they are
living on a smaller space scale. We validate our construction by proving a
convergence theorem of the microscopic system to the given continuum, as the
scale parameter goes to zero.Comment: 20 page
Review of Some Promising Fractional Physical Models
Fractional dynamics is a field of study in physics and mechanics
investigating the behavior of objects and systems that are characterized by
power-law non-locality, power-law long-term memory or fractal properties by
using integrations and differentiation of non-integer orders, i.e., by methods
of the fractional calculus. This paper is a review of physical models that look
very promising for future development of fractional dynamics. We suggest a
short introduction to fractional calculus as a theory of integration and
differentiation of non-integer order. Some applications of
integro-differentiations of fractional orders in physics are discussed. Models
of discrete systems with memory, lattice with long-range inter-particle
interaction, dynamics of fractal media are presented. Quantum analogs of
fractional derivatives and model of open nano-system systems with memory are
also discussed.Comment: 38 pages, LaTe
Non-local fractional model of rate independent plasticity
In the paper the generalisation of classical rate independent plasticity
using fractional calculus is presented. This new formulation is non-local due
to properties of applied fractional differential operator during definition of
kinematics. In the description small fractional strains assumption is hold
together with additive decomposition of total fractional strains into elastic
and plastic parts. Classical local rate independent plasticity is recovered as
a special case
A Generalized Fractional Calculus of Variations
We study incommensurate fractional variational problems in terms of a
generalized fractional integral with Lagrangians depending on classical
derivatives and generalized fractional integrals and derivatives. We obtain
necessary optimality conditions for the basic and isoperimetric problems,
transversality conditions for free boundary value problems, and a generalized
Noether type theorem.Comment: This is a preprint of a paper whose final and definitive form will
appear in Control and Cybernetics. Paper submitted 01-Oct-2012; revised
25-March-2013; accepted for publication 17-April-201
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