Fractional order of Legendre-type matrix polynomials

Autor: M. Zayed, M. Hidan, M. Abdalla, M. Abul-Ez
Jazyk: angličtina
Rok vydání: 2020
Předmět:
Zdroj: Advances in Difference Equations, Vol 2020, Iss 1, Pp 1-13 (2020)
Druh dokumentu: article
ISSN: 1687-1847
DOI: 10.1186/s13662-020-02975-5
Popis: Abstract Recently, special functions of fractional order calculus have had many applications in various areas of mathematical analysis, physics, probability theory, optimization theory, graph theory, control systems, earth sciences, and engineering. Very recently, Zayed et al. (Mathematics 8:136, 2020) introduced the shifted Legendre-type matrix polynomials of arbitrary fractional orders and their various applications utilizing Rodrigues matrix formulas. In this line of research, we use the fractional order of Rodrigues formula to provide further investigation on such Legendre polynomials from a different point of view. Some properties, such as hypergeometric representations, continuation properties, recurrence relations, and differential equations, are derived. Moreover, Laplace’s first integral form and orthogonality are obtained.
Databáze: Directory of Open Access Journals
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