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 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].

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.

scholarly journals New Chebyshev type inequalities via a general family of fractional integral operators with a modified Mittag-Leffler kernel

2021 ◽  
Vol 6 (10) ◽  
pp. 11167-11186
Author(s):  
Hari M. Srivastava ◽  
◽  
Artion Kashuri ◽  
Pshtiwan Othman Mohammed ◽  
Abdullah M. Alsharif ◽  
...  
Keyword(s):  
Fractional Integral ◽  
Integral Operators ◽  
Fractional Integrals ◽  
Chebyshev Inequality ◽  
Fractional Integral Operators ◽  
General Family ◽  
Chebyshev Functional ◽  
Bounded Below

<abstract><p>The main goal of this article is first to introduce a new generalization of the fractional integral operators with a certain modified Mittag-Leffler kernel and then investigate the Chebyshev inequality via this general family of fractional integral operators. We improve our results and we investigate the Chebyshev inequality for more than two functions. We also derive some inequalities of this type for functions whose derivatives are bounded above and bounded below. In addition, we establish an estimate for the Chebyshev functional by using the new fractional integral operators. Finally, we find similar inequalities for some specialized fractional integrals keeping some of the earlier results in view.</p></abstract>

scholarly journals Fractional Hermite–Hadamard–Fejer Inequalities for a Convex Function with Respect to an Increasing Function Involving a Positive Weighted Symmetric Function

Symmetry ◽  
2020 ◽  
Vol 12 (9) ◽  
pp. 1503 ◽  
Author(s):  
Pshtiwan Othman Mohammed ◽  
Thabet Abdeljawad ◽  
Artion Kashuri
Keyword(s):  
Fractional Calculus ◽  
Convex Function ◽  
Symmetric Function ◽  
Fractional Integral ◽  
Integral Inequalities ◽  
Fractional Integrals ◽  
Fractional Operators ◽  
Important Direction ◽  
Increasing Function

There have been many different definitions of fractional calculus presented in the literature, especially in recent years. These definitions can be classified into groups with similar properties. An important direction of research has involved proving inequalities for fractional integrals of particular types of functions, such as Hermite–Hadamard–Fejer (HHF) inequalities and related results. Here we consider some HHF fractional integral inequalities and related results for a class of fractional operators (namely, the weighted fractional operators), which apply to function of convex type with respect to an increasing function involving a positive weighted symmetric function. We can conclude that all derived inequalities in our study generalize numerous well-known inequalities involving both classical and Riemann–Liouville fractional integral inequalities.

scholarly journals Some Fractional Operators with the Generalized Bessel–Maitland Function

2020 ◽  
Vol 2020 ◽  
pp. 1-15
Author(s):  
R. S. Ali ◽  
S. Mubeen ◽  
I. Nayab ◽  
Serkan Araci ◽  
G. Rahman ◽  
...  
Keyword(s):  
Fractional Calculus ◽  
Liouville Operator ◽  
Fractional Integral ◽  
Integral Transform ◽  
Inverse Operator ◽  
Integral Operators ◽  
Fractional Operators ◽  
Fractional Integral Operators

In this paper, we aim to determine some results of the generalized Bessel–Maitland function in the field of fractional calculus. Here, some relations of the generalized Bessel–Maitland functions and the Mittag-Leffler functions are considered. We develop Saigo and Riemann–Liouville fractional integral operators by using the generalized Bessel–Maitland function, and results can be seen in the form of Fox–Wright functions. We establish a new operator Zν,η,ρ,γ,w,a+μ,ξ,m,σϕ and its inverse operator Dν,η,ρ,γ,w,a+μ,ξ,m,σϕ, involving the generalized Bessel–Maitland function as its kernel, and also discuss its convergence and boundedness. Moreover, the Riemann–Liouville operator and the integral transform (Laplace) of the new operator have been developed.

Fractional powers of operators and Riesz fractional integrals

1989 ◽  
Vol 112 (3-4) ◽  
pp. 237-247 ◽  
Author(s):  
S. E. Schiavone
Keyword(s):  
Banach Spaces ◽  
Fractional Integral ◽  
Integral Operators ◽  
Fractional Integrals ◽  
Fréchet Spaces ◽  
Test Functions ◽  
Fractional Powers ◽  
Fractional Integral Operators ◽  
Fractional Powers Of Operators

SynopsisIn this paper, a theory of fractional powers of operators due to Balakrishnan, which is valid for certain operators on Banach spaces, is extended to Fréchet spaces. The resultingtheory is shown to be more general than that developed in an earlier approach by Lamb, and is applied to obtain mapping properties of certain Riesz fractional integral operators on spaces of test functions.

scholarly journals Certain Chebyshev Type Integral Inequalities Involving Hadamard’s Fractional Operators

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
Sotiris K. Ntouyas ◽  
Sunil D. Purohit ◽  
Jessada Tariboon
Keyword(s):  
Fractional Integral ◽  
Integral Operators ◽  
Integral Inequalities ◽  
Fractional Operators ◽  
Weighted Version ◽  
Fractional Integral Operators ◽  
Differentiable Functions ◽  
Type Integral ◽  
Chebyshev Functional

We establish certain new fractional integral inequalities for the differentiable functions whose derivatives belong to the spaceLp([1,∞)), related to the weighted version of the Chebyshev functional, involving Hadamard’s fractional integral operators. As an application, particular results have been also established.

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