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Open AccessArticle

Fractional Supersymmetric Hermite Polynomials

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Department of Mathematics, College of Sciences, King Saud University, P. O. Box 2455 Riyadh 11451, Saudi Arabia
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Department of Statistics & OR, King Saud University, P.O. Box 2455, Riyadh 11451, Saudi Arabia
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Faculté des Sciences de Tunis, LR11ES11 Laboratoire d’Analyse Mathématiques et Applications, Université de Tunis El Manar, Tunis 2092, Tunisia
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Author to whom correspondence should be addressed.
Mathematics 2020, 8(2), 193; https://doi.org/10.3390/math8020193
Received: 12 December 2019 / Revised: 27 January 2020 / Accepted: 31 January 2020 / Published: 5 February 2020
(This article belongs to the Special Issue Polynomials: Theory and Applications)
We provide a realization of fractional supersymmetry quantum mechanics of order r, where the Hamiltonian and the supercharges involve the fractional Dunkl transform as a Klein type operator. We construct several classes of functions satisfying certain orthogonality relations. These functions can be expressed in terms of the associated Laguerre orthogonal polynomials and have shown that their zeros are the eigenvalues of the Hermitian supercharge. We call them the supersymmetric generalized Hermite polynomials.
Keywords: orthogonal polynomials; difference-differential operator; supersymmetry orthogonal polynomials; difference-differential operator; supersymmetry
MDPI and ACS Style

Bouzeffour, F.; Jedidi, W. Fractional Supersymmetric Hermite Polynomials. Mathematics 2020, 8, 193.

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