Fractional order of Legendre-type matrix polynomials

Advances in Difference Equations

M. Hidan¹  M. Zayed¹  M. Abdalla²  M. Abul-Ez³ 

[1] Department of Mathematics, College of Science, King Khalid University, P.O. Box 9004, 61413, Abha, Saudi Arabia;Department of Mathematics, College of Science, King Khalid University, P.O. Box 9004, 61413, Abha, Saudi Arabia;Department of Mathematics, Faculty of Science, South Valley University, 83523, Qena, Egypt;Mathematics Department, Faculty of Science, Sohag University, Sohag, 82524, Sohag, Egypt;

关键词: Special matrix functions;    Fractional calculus;    Legendre matrix polynomials;    Rodrigues-type formula;    15A15;    33C70;    33C05;    33D15;   

DOI  :  10.1186/s13662-020-02975-5

来源: Springer

【 摘 要 】

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.

【 授权许可】

CC BY