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Fractional Calculus and Applied Analysis

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Reflection symmetric Erdélyi-Kober type operators — A quasi-particle interpretation

1GigaHedron, Berliner Ring 80, D-63303, Dreieich, Germany

© 2014 Diogenes Co., Sofia. This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License. (CC BY-NC-ND 3.0)

Citation Information: Fractional Calculus and Applied Analysis. Volume 17, Issue 4, Pages 1215–1228, ISSN (Online) 1314-2224, ISSN (Print) 1311-0454, DOI: https://doi.org/10.2478/s13540-014-0221-1, September 2014

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The reflection symmetric Erdélyi-Kober type fractional integral operators are used to construct fractional quasi-particle generators. The eigenfunctions and eigenvalues of these operators are given analytically. A set of fractional creation- and annihilation-operators is defined and the properties of the corresponding free Hamiltonian are investigated. Analogously to the classical approach for interacting multi-particle systems, the results are interpreted as a fractional quantum model for a description of residual interactions of pairing type.

MSC: 26A33; Secondary: 70Hxx, 37Kxx, 81Q35, 81Q60

Keywords: generalized fractional calculus; shifted Riesz integrals; Erdélyi-Kober integrals; fractional operators; Fock space; quasiparticle; pairing-Hamiltonian

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