On the Fractional Order Rodrigues Formula for the Shifted Legendre-Type Matrix Polynomials

Mohra Zayed, Mahmoud Abul-Ez, Mohamed Abdalla and Nasser Saad
Additional contact information
Mohra Zayed: Mathematics Department, College of Science, King Khalid University, Abha 61413, Saudi Arabia
Mahmoud Abul-Ez: Mathematics Department, Faculty of Science, Sohag University, Sohag 82524, Egypt
Mohamed Abdalla: Mathematics Department, College of Science, King Khalid University, Abha 61413, Saudi Arabia
Nasser Saad: School of Mathematical and Computational Sciences, University of Prince Edward Island, Charlottetown, PE C1A 4P3, Canada

Mathematics, 2020, vol. 8, issue 1, 1-23

Abstract: The generalization of Rodrigues’ formula for orthogonal matrix polynomials has attracted the attention of many researchers. This generalization provides new integral and differential representations in addition to new mathematical results that are useful in theoretical and numerical computations. Using a recently studied operational matrix for shifted Legendre polynomials with the variable coefficients fractional differential equations, the present work introduces the shifted Legendre-type matrix polynomials of arbitrary (fractional) orders utilizing some Rodrigues matrix formulas. Many interesting mathematical properties of these matrix polynomials are investigated and reported in this paper, including recurrence relations, differential properties, hypergeometric function representation, and integral representation. Furthermore, the orthogonality property of these polynomials is examined in some particular cases. The developed results provide a matrix framework that generalizes and enhances the corresponding scalar version and introduces some new properties with proposed applications. Some of these applications are explored in the present work.

Keywords: rodrigues-type formula; fractional calculus; Legendre matrix polynomials; the shifted Legendre matrix polynomials (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
https://www.mdpi.com/2227-7390/8/1/136/pdf (application/pdf)
https://www.mdpi.com/2227-7390/8/1/136/ (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:gam:jmathe:v:8:y:2020:i:1:p:136-:d:310169

Access Statistics for this article

Mathematics is currently edited by Ms. Emma He

More articles in Mathematics from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().