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Fractional Calculus and Applied Analysis

Editor-in-Chief: Kiryakova, Virginia


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Volume 15, Issue 3

Issues

Towards a combined fractional mechanics and quantization

Agnieszka Malinowska / Delfim Torres
  • Center for Research and Development in Mathematics and Applications Department of Mathematics, University of Aveiro, 3810-193, Aveiro, Portugal
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Published Online: 2012-06-30 | DOI: https://doi.org/10.2478/s13540-012-0029-9

Abstract

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.

MSC: Primary 26A33, 49K05; Secondary 49S05

Keywords: fractional canonical formalism; Hamiltonian approach; variational principles of physics; nonconservative systems; combined fractional derivatives; variational calculus

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About the article

Published Online: 2012-06-30

Published in Print: 2012-09-01


Citation Information: Fractional Calculus and Applied Analysis, Volume 15, Issue 3, Pages 407–417, ISSN (Online) 1314-2224, ISSN (Print) 1311-0454, DOI: https://doi.org/10.2478/s13540-012-0029-9.

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© 2012 Diogenes Co., Sofia. This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License. BY-NC-ND 3.0

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