scholarly journals Some Multidimensional Fractional Integral Operators Involving a General Class of Polynomials

1995 ◽  
Vol 193 (2) ◽  
pp. 373-389 ◽  
Author(s):  
H.M. Srivastava ◽  
R.K. Saxena ◽  
J. Ram
Keyword(s):  
General Class ◽  
Fractional Integral ◽  
Integral Operators ◽  
Fractional Integral Operators ◽  
General Class Of Polynomials

scholarly journals Fractional calculus pertaining to multivariable Aleph-function

2022 ◽  
Vol 40 ◽  
pp. 1-10
Author(s):  
Dinesh Kumar ◽  
Frederic Ayant
Keyword(s):  
Integral Operator ◽  
Fractional Calculus ◽  
General Class ◽  
Fractional Integral ◽  
Integral Operators ◽  
Fractional Integral Operator ◽  
General Nature ◽  
Fractional Integral Operators ◽  
Mellin Transforms ◽  
General Class Of Polynomials

In this paper we study a pair of unied and extended fractional integral operator involving the multivariable Aleph-function, Aleph-function and general class of polynomials. During this study, we establish ve theorems pertaining to Mellin transforms of these operators. Furthers, some properties of these operators have also been investigated. On account of the general nature of the functions involved herein, a large number of (known and new) fractional integral operators involved simpler functions can also be obtained . We will quote the particular case concerning the multivariable I-function dened by Sharma and Ahmad [20] and the I-function of one variable dened by Saxena [13].

On Ostrowski type inequalities

2016 ◽  
Vol 56 (1) ◽  
pp. 5-27 ◽  
Author(s):  
Ravi P. Agarwal ◽  
Min-Jie Luo ◽  
R.K. Raina
Keyword(s):  
Hypergeometric Function ◽  
General Class ◽  
Fractional Integral ◽  
Integral Operators ◽  
Generalized Hypergeometric Function ◽  
Fractional Integral Operators ◽  
Special Cases

Abstract In this paper, new forms of Ostrowski type inequalities are established for a general class of fractional integral operators. The main results are used to derive Ostrowski type inequalities involving the familiar Riemann-Liouville fractional integral operators and other important integral operators. We further obtain similar types of inequalities for the integral operators whose kernels are the Fox-Wright generalized hypergeometric function. Several consequences and special cases of some of the results including applications to Stolarsky’s means are also pointed out.

scholarly journals Fractional calculus pertaining to multivariable I-function defined by Prathima

2019 ◽  
Vol 15 (2) ◽  
pp. 61-73
Author(s):  
D. Kumar ◽  
F. Y. Ayant
Keyword(s):  
Integral Operator ◽  
Fractional Calculus ◽  
General Class ◽  
Fractional Integral ◽  
Integral Operators ◽  
Fractional Integral Operator ◽  
General Nature ◽  
Fractional Integral Operators ◽  
Mellin Transforms

Abstract In this paper, we study a pair of unified and extended fractional integral operator involving the multivariable I-functions and general class of multivariable polynomials. Here, we use Mellin transforms to obtain our main results. Certain properties of these operators concerning to their Mellin-transforms have been investigated. On account of the general nature of the functions involved herein, a large number of known (may be new also) fractional integral operators involved simpler functions can be obtained. We will also quote the particular case of the multivariable H-function.

scholarly journals Fractional integral operators involving the product of Srivastava polynomials and Srivastava-Panda multivariable $ H $ -functions of generalized arguments

2008 ◽  
Vol 39 (2) ◽  
pp. 131-136
Author(s):  
V. B. L. Chaurasia ◽  
S. C. Pandey
Keyword(s):  
General Class ◽  
Fractional Integral ◽  
Integral Operators ◽  
Proper Choice ◽  
Fractional Integral Operators

 The paper deals with two fractionalintegral formulae involving the product of a general class ofpolynomials and multivariate $H$-function. The first involves theoperator $_cI_z^v[f(z)]$ whereas second is associated with theintegral operator $I_z^{\eta, v}[f(z)]$. In our fractional integralformulae we have taken all the functions and polynomials with ageneralized argument. The formulae, we have introduced here, are incompact form and basic in nature. A number of known and new resultshave been obtained by proper choice of parameters. For the sake ofillustration, we record here some particular cases of our mainresults.

scholarly journals Fractional q -Integral Operators for the Product of a q -Polynomial and q -Analogue of the I -Functions and Their Applications

2021 ◽  
Vol 2021 ◽  
pp. 1-9
Author(s):  
V.K. Vyas ◽  
Ali A. Al-Jarrah ◽  
D. L. Suthar ◽  
Nigussie Abeye
Keyword(s):  
General Class ◽  
Fractional Integral ◽  
Integral Operators ◽  
Fractional Integrals ◽  
Fractional Operators ◽  
Integral Image ◽  
General Class Of Polynomials ◽  
The Relationship

In this article, we derive four theorems concerning the fractional integral image for the product of the q -analogue of general class of polynomials with the q -analogue of the I -functions. To illustrate our main results, we use q -fractional integrals of Erdélyi–Kober type and generalized Weyl type fractional operators. The study concludes with a variety of results that can be obtained by using the relationship between the Erdélyi–Kober type and the Riemann–Liouville q -fractional integrals, as well as the relationship between the generalized Weyl type and the Weyl type q -fractional integrals.

scholarly journals On integral inequalities related to the weighted and the extended Chebyshev functionals involving different fractional operators

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Barış Çelik ◽  
Mustafa Ç. Gürbüz ◽  
M. Emin Özdemir ◽  
Erhan Set
Keyword(s):  
Fractional Integral ◽  
Integral Operators ◽  
Integral Inequalities ◽  
Fractional Operators ◽  
Fractional Integral Operators

AbstractThe role of fractional integral operators can be found as one of the best ways to generalize classical inequalities. In this paper, we use different fractional integral operators to produce some inequalities for the weighted and the extended Chebyshev functionals. The results are more general than the available classical results in the literature.

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