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Towards a combined fractional mechanics and quantization

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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.

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Authors and Affiliations

  1. Faculty of Computer Science, Białystok University of Technology, 15-351, Białystok, Poland

    Agnieszka B. Malinowska

  2. Center for Research and Development in Mathematics and Applications Department of Mathematics, University of Aveiro, 3810-193, Aveiro, Portugal

    Delfim F. M. Torres

Authors
  1. Agnieszka B. Malinowska
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  2. Delfim F. M. Torres
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Correspondence to Agnieszka B. Malinowska.

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Malinowska, A.B., Torres, D.F.M. Towards a combined fractional mechanics and quantization. fcaa 15, 407–417 (2012). https://doi.org/10.2478/s13540-012-0029-9

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  • DOI: https://doi.org/10.2478/s13540-012-0029-9

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