scholarly journals On 2-Variables Konhauser Matrix Polynomials and Their Fractional Integrals

Mathematics ◽  
2020 ◽  
Vol 8 (2) ◽  
pp. 232 ◽  
Author(s):  
Ahmed Bakhet ◽  
Fuli He
Keyword(s):  
Integral Representations ◽  
Fractional Integrals ◽  
Matrix Polynomials ◽  
Generating Matrix ◽  
Finite Sum

In this paper, we first introduce the 2-variables Konhauser matrix polynomials; then, we investigate some properties of these matrix polynomials such as generating matrix relations, integral representations, and finite sum formulae. Finally, we obtain the fractional integrals of the 2-variables Konhauser matrix polynomials.

scholarly journals On new extensions of the generalized Hermite matrix polynomials

2019 ◽  
Vol 22 (2) ◽  
pp. 203-222
Author(s):  
Ayman Shehata
Keyword(s):  
Integral Representations ◽  
Matrix Functions ◽  
Matrix Polynomials ◽  
Summation Formulae ◽  
Summation Formulas ◽  
Fractional Calculus Operators ◽  
Generating Matrix Functions ◽  
Hermite Matrix ◽  
Generating Matrix ◽  
Matrix Recurrence Relations

Various families of generating matrix functions have been established in diverse ways. The objective of the present paper is to investigate these generalized Hermite matrix polynomials, and derive some important results for them, such as, the generating matrix functions, matrix recurrence relations, an expansion of xnI, finite summation formulas, addition theorems, integral representations, fractional calculus operators, and certain other implicit summation formulae.

scholarly journals Some new results for Jacobi matrix polynomials

Filomat ◽  
2013 ◽  
Vol 27 (4) ◽  
pp. 713-719 ◽  
Author(s):  
Bayram Çekim ◽  
Abdullah Altin ◽  
Rabia Aktaş
Keyword(s):  
Matrix Function ◽  
Recurrence Relations ◽  
Jacobi Matrix ◽  
Integral Representations ◽  
Matrix Polynomials ◽  
Generating Matrix

The main aim of this paper is to obtain some recurrence relations and generating matrix function for Jacobi matrix polynomials (JMP). Also, various integral representations satisfied by JMP are derived.

scholarly journals On the Extended Hypergeometric Matrix Functions and Their Applications for the Derivatives of the Extended Jacobi Matrix Polynomial

2020 ◽  
Vol 2020 ◽  
pp. 1-8 ◽  
Author(s):  
Fuli He ◽  
Ahmed Bakhet ◽  
M. Abdalla ◽  
M. Hidan
Keyword(s):  
Matrix Function ◽  
Matrix Polynomial ◽  
Jacobi Matrix ◽  
Integral Representations ◽  
Matrix Functions ◽  
Matrix Polynomials ◽  
Special Cases ◽  
Generating Matrix Functions ◽  
Generating Matrix ◽  
Derivatives Of

In this paper, we obtain some generating matrix functions and integral representations for the extended Gauss hypergeometric matrix function EGHMF and their special cases are also given. Furthermore, a specific application for the extended Gauss hypergeometric matrix function which includes Jacobi matrix polynomials is constructed.

Integral Representations and Continuous Projectors in Some Spaces of Analytic and Pluriharmonic Functions

2008 ◽  
Vol 15 (4) ◽  
pp. 739-752
Author(s):  
Gigla Oniani ◽  
Lamara Tsibadze
Keyword(s):  
Integral Representations ◽  
Fractional Integrals ◽  
Boundary Values ◽  
Pluriharmonic Functions

Abstract We consider analytic and pluriharmonic functions belonging to the classes 𝐵𝑝(Ω) and 𝑏𝑝(Ω) and defined in the ball . The theorems established in the paper make it possible to obtain some integral representations of functions of the above-mentioned classes. The existence of bounded projectors from the space 𝐿(ρ, Ω) into the space 𝐵𝑝(Ω) and from the space 𝐿(ρ, Ω) into the space 𝑏𝑝(Ω) is proved. Also, consideration is given to the existence of boundary values of fractional integrals of functions of the spaces 𝐵𝑝(Ω) and 𝑏𝑝(Ω).

scholarly journals Q-matrix polynomials in several variables

Filomat ◽  
2015 ◽  
Vol 29 (9) ◽  
pp. 2059-2067 ◽  
Author(s):  
Bayram Çekim
Keyword(s):  
Matrix Functions ◽  
Matrix Polynomials ◽  
Several Variables ◽  
Generating Matrix Functions ◽  
Hermite Matrix ◽  
Q Matrix ◽  
Generating Matrix

In the present paper, we define q-matrix polynomials in several variables which reduces Chan-Chyan-Srivastava and Lagrange-Hermite matrix polynomials in [6]. Then several results involving generating matrix functions for these matrix polynomials are derived.

scholarly journals The J-Generalized P - K Mittag-Leffler Function

2020 ◽  
Author(s):  
Kuldeep Singh Gehlot ◽  
Anjana Bhandari
Keyword(s):  
Mellin Transform ◽  
Integral Representations ◽  
Fractional Integrals ◽  
Linear Differential ◽  
Euler Transform ◽  
Relationship Of ◽  
The Relationship ◽  
Homogeneous Linear ◽  
Homogeneous Linear Differential Equation ◽  
Differential And Integral Equations

We know that the classical Mittag-Leffler function play an important role as solution of fractional order differential and integral equations. We introduce the j-generalized p - k Mittag-Leffler function. We evaluate the second order differential recurrence relation and four different integral representations and introduce a homogeneous linear differential equation whose one of the solution is the j-generalized p-k Mittag-Leffler function. Also we evaluate the certain relations that exist between j-generalized p - k Mittag-Leffler function and Riemann-Liouville fractional integrals and derivatives. We evaluate Mellin-Barnes integral representation of j-generalized p-k Mittag-Le er Function. The relationship of j-generalized p-k Mittag-Leffler Function with Fox H-Function and Wright hypergeometric function is also establish. we obtained its Euler transform, Laplace Transform and Mellin transform. Finally we derive some particular cases.

Analytical properties of the two-variables Jacobi matrix polynomials with applications

2021 ◽  
Vol 54 (1) ◽  
pp. 178-188
Author(s):  
Mohamed Abdalla ◽  
Muajebah Hidan
Keyword(s):  
Recurrence Relations ◽  
Jacobi Matrix ◽  
Matrix Functions ◽  
Type Formula ◽  
Matrix Polynomials ◽  
Analytical Properties ◽  
Generating Matrix Functions ◽  
Generating Matrix

Abstract In the current study, we introduce the two-variable analogue of Jacobi matrix polynomials. Some properties of these polynomials such as generating matrix functions, a Rodrigue-type formula and recurrence relations are also derived. Furthermore, some relationships and applications are reported.

scholarly journals Analytical Properties of the Generalized Heat Matrix Polynomials Associated with Fractional Calculus

2021 ◽  
Vol 2021 ◽  
pp. 1-7
Author(s):  
Mohamed Abdalla ◽  
Salah Mahmoud Boulaaras
Keyword(s):  
Fractional Calculus ◽  
Integral Transforms ◽  
Matrix Functions ◽  
Matrix Polynomials ◽  
Matrix Version ◽  
Analytical Properties ◽  
Fractional Calculus Operators ◽  
Finite Sums ◽  
Generating Matrix Functions ◽  
Generating Matrix

In this paper, we introduce a matrix version of the generalized heat polynomials. Some analytic properties of the generalized heat matrix polynomials are obtained including generating matrix functions, finite sums, and Laplace integral transforms. In addition, further properties are investigated using fractional calculus operators.

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