scholarly journals Certain Unified Integrals Involving a Multivariate Mittag–Leffler Function

Axioms ◽  
2021 ◽  
Vol 10 (2) ◽  
pp. 81
Author(s):  
Shilpi Jain ◽  
Ravi P. Agarwal ◽  
Praveen Agarwal ◽  
Prakash Singh
Keyword(s):  
Integral Formulas ◽  
Special Cases

A remarkably large number of unified integrals involving the Mittag–Leffler function have been presented. Here, with the same technique as Choi and Agarwal, we propose the establishment of two generalized integral formulas involving a multivariate generalized Mittag–Leffler function, which are expressed in terms of the generalized Lauricella series due to Srivastava and Daoust. We also present some interesting special cases.

scholarly journals Pathway fractional integral operators of generalized k-wright function and k4-function

2017 ◽  
Vol 35 (2) ◽  
pp. 235 ◽  
Author(s):  
Dinesh Kumar ◽  
Ram Kishore Saxena ◽  
Jitendra Daiya
Keyword(s):  
Fractional Integral ◽  
Fractional Integration ◽  
Integral Operators ◽  
Wright Function ◽  
Finite Product ◽  
Fractional Integral Operators ◽  
Integral Formulas ◽  
Fractional Integration Operator ◽  
Composition Formula ◽  
Special Cases

In the present work we introduce a composition formula of the pathway fractional integration operator with finite product of generalized K-Wright function and K4-function. The obtained results are in terms of generalized Wright function.Certain special cases of the main results given here are also considered to correspond with some known and new (presumably) pathway fractional integral formulas.

scholarly journals Certain Integral Transform and Fractional Integral Formulas for the Generalized Gauss Hypergeometric Functions

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
Junesang Choi ◽  
Praveen Agarwal
Keyword(s):  
Hypergeometric Functions ◽  
Fractional Integral ◽  
Integral Transform ◽  
Special Functions ◽  
Integral Transforms ◽  
Integral Formulas ◽  
Special Cases

A remarkably large number of integral transforms and fractional integral formulas involving various special functions have been investigated by many authors. Very recently, Agarwal gave some integral transforms and fractional integral formulas involving theFp(α,β)(·). In this sequel, using the same technique, we establish certain integral transforms and fractional integral formulas for the generalized Gauss hypergeometric functionsFp(α,β,m)(·). Some interesting special cases of our main results are also considered.

scholarly journals Certain Fractional Integral Formulas Involving the Product of Generalized Bessel Functions

2013 ◽  
Vol 2013 ◽  
pp. 1-9 ◽  
Author(s):  
D. Baleanu ◽  
P. Agarwal ◽  
S. D. Purohit
Keyword(s):  
Bessel Function ◽  
Fractional Integral ◽  
Bessel Functions ◽  
Fractional Integration ◽  
Fractional Integrals ◽  
General Character ◽  
Generalized Bessel Function ◽  
Integral Formulas ◽  
Generalized Bessel Functions ◽  
Special Cases

We apply generalized operators of fractional integration involving Appell’s functionF3(·)due to Marichev-Saigo-Maeda, to the product of the generalized Bessel function of the first kind due to Baricz. The results are expressed in terms of the multivariable generalized Lauricella functions. Corresponding assertions in terms of Saigo, Erdélyi-Kober, Riemann-Liouville, and Weyl type of fractional integrals are also presented. Some interesting special cases of our two main results are presented. We also point out that the results presented here, being of general character, are easily reducible to yield many diverse new and known integral formulas involving simpler functions.

scholarly journals On certain integral formulas involving the product of Bessel function and Jacobi polynomial

2016 ◽  
Vol 47 (3) ◽  
pp. 339-349 ◽  
Author(s):  
Nabi Ullah Khan ◽  
Mohd Ghayasuddin ◽  
Talha Usman
Keyword(s):  
Bessel Function ◽  
Legendre Polynomial ◽  
Jacobi Polynomial ◽  
Cosine Function ◽  
Ultraspherical Polynomial ◽  
Integral Formulas ◽  
Interesting Connection ◽  
Special Cases ◽  
Gegenbauer Polynomial

In the present paper, we establish some interesting integrals involving the product of Bessel function of the first kind with Jacobi polynomial, which are expressed in terms of Kampe de Feriet and Srivastava and Daoust functions. Some other integrals involving the product of Bessel (sine and cosine) function with ultraspherical polynomial, Gegenbauer polynomial, Tchebicheff polynomial, and Legendre polynomial are also established as special cases of our main results. Further, we derive an interesting connection between Kampe de Feriet and Srivastava and Daoust functions.

scholarly journals Certain families of integral formulas involving Struve functions

2017 ◽  
Vol 37 (3) ◽  
pp. 27-35
Author(s):  
Junesang Choi ◽  
Nisar Koottakkaran Sooppy
Keyword(s):  
Bessel Functions ◽  
Wright Function ◽  
Hyperbolic Functions ◽  
Integral Formulas ◽  
Special Cases ◽  
Struve Functions

Recently, a large number of integral formulas involving Bessel functions and their extensions have been investigated. The objective of this paper is to establish four classes of integral formulas associated with the Struve functions, which are expressed in terms of the Fox-Wright function. Among a variety of special cases of the main results, we present only six integral formulas involving trigonometric and hyperbolic functions.

scholarly journals On Generalized Fractional Integral Operators and the Generalized Gauss Hypergeometric Functions

2014 ◽  
Vol 2014 ◽  
pp. 1-5 ◽  
Author(s):  
Dumitru Baleanu ◽  
Praveen Agarwal
Keyword(s):  
Hypergeometric Functions ◽  
Fractional Integral ◽  
Integral Transform ◽  
Special Functions ◽  
Fractional Integration ◽  
Fractional Integral Operators ◽  
Integral Formulas ◽  
Special Cases ◽  
Generalized Fractional Integral ◽  
Generalized Fractional Integral Operators

A remarkably large number of fractional integral formulas involving the number of special functions, have been investigated by many authors. Very recently, Agarwal (National Academy Science Letters) gave some integral transform and fractional integral formulas involving theFpα,β·. In this sequel, here, we aim to establish some image formulas by applying generalized operators of the fractional integration involving Appell’s functionF3(·)due to Marichev-Saigo-Maeda. Some interesting special cases of our main results are also considered.

scholarly journals Unified integral associated with the generalized V-function

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
S. Chandak ◽  
S. K. Q. Al-Omari ◽  
D. L. Suthar
Keyword(s):  
Bessel Function ◽  
Hypergeometric Function ◽  
Exponential Function ◽  
Special Functions ◽  
General Nature ◽  
Generalized Hypergeometric Function ◽  
Generalized Bessel Function ◽  
Integral Formulas ◽  
Special Cases ◽  
Lommel Function

Abstract In this paper, we present two new unified integral formulas involving a generalized V-function. Some interesting special cases of the main results are also considered in the form of corollaries. Due to the general nature of the V-function, several results involving different special functions such as the exponential function, the Mittag-Leffler function, the Lommel function, the Struve function, the Wright generalized Bessel function, the Bessel function and the generalized hypergeometric function are obtained by specializing the parameters in the presented formulas. More results are also discussed in detail.

scholarly journals ON GENERAL EULERIAN INTEGRAL FORMULAS AND FRACTIONAL INTEGRATION

1999 ◽  
Vol 30 (2) ◽  
pp. 155-164
Author(s):  
K. C. GUPTA ◽  
S. P. GOYAL ◽  
R. K. LADDHA
Keyword(s):  
Integral Operator ◽  
Infinite Series ◽  
Fractional Integral ◽  
Integral Formula ◽  
Polynomial System ◽  
Fractional Integration ◽  
Compact Form ◽  
Integral Formulas ◽  
Special Cases ◽  
Type Integral

In the present work, we evaluate a unified Eulerian type integral whose integrand involves the product of a polynomial system and the multivariable H-function having general arguments. Our integral formula encompasses a very large number of integrals and provides interesting unifieation and extensions of several known (e.g., [1], [3], [4], [5], [9], [11], etc.) and new results. Since the integral has been given in a compact form free from infinite series, it is likely to prove useful in applications. Three special cases of the main integral (which are also sufficiently general in nature and are of interest in themselves) have also been given. Finally, the main integral formula has been expressed as a fractional integral operator to make it more useful in applications.

scholarly journals Generalized q-Laguerre type polynomials and q-partial differential equations

Filomat ◽  
2019 ◽  
Vol 33 (5) ◽  
pp. 1403-1415
Author(s):  
Da-Wei Niu
Keyword(s):  
Partial Differential Equations ◽  
Differential Operator ◽  
Differential Equations ◽  
Generating Functions ◽  
Final Section ◽  
Laguerre Polynomials ◽  
Hermite Polynomials ◽  
Partial Differential ◽  
Integral Formulas ◽  
Special Cases

In this paper we define the q-Laguerre type polynomials Un(x; y; z; q), which include q-Laguerre polynomials, generalized Stieltjes-Wigert polynomials, little q-Laguerre polynomials and q-Hermite polynomials as special cases. We also establish a generalized q-differential operator, with which we build the relations between analytic functions and Un(x; y; z; q) by using certain q-partial differential equations. Therefore, the corresponding conclusions about q-Laguerre polynomials, little q-Laguerre polynomials and q-Hermite polynomials are gained as corollaries. As applications, some generating functions and generalized Andrews-Askey integral formulas are given in the final section.

scholarly journals A New Class of Integrals Involving Extended Mittag–Leffler Functions

2017 ◽  
Author(s):  
Gauhar Rahman ◽  
Abdul Ghaffar ◽  
Kottakkaran Sooppy Nisar ◽  
Shahid Mubeen
Keyword(s):  
Integral Formula ◽  
Type Function ◽  
New Class ◽  
Integral Formulas ◽  
Special Cases

The main aim of this paper is to establish two generalized integral formulas involving the extended Mittag–Leffler function based on the well known Lavoie and Trottier integral formula and the obtain results are express in term of extended Wright-type function. Also, we establish certain special cases of our main result.

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