Integral Inequalities Associated with Gauss Hypergeometric Function Fractional Integral Operators

2016 ◽  
Vol 88 (1) ◽  
pp. 27-31 ◽  
Author(s):  
R. K. Saxena ◽  
S. D. Purohit ◽  
Dinesh Kumar
Keyword(s):  
Hypergeometric Function ◽  
Fractional Integral ◽  
Integral Operators ◽  
Integral Inequalities ◽  
Gauss Hypergeometric Function ◽  
Fractional Integral Operators

scholarly journals On Fractional Integral Inequalities Involving Hypergeometric Operators

2014 ◽  
Vol 2014 ◽  
pp. 1-5 ◽  
Author(s):  
D. Baleanu ◽  
S. D. Purohit ◽  
Praveen Agarwal
Keyword(s):  
Hypergeometric Function ◽  
Fractional Integral ◽  
Integral Operators ◽  
Integral Inequalities ◽  
Gauss Hypergeometric Function ◽  
Liouville Type ◽  
Fractional Integral Operators ◽  
Special Cases ◽  
Chebyshev Functional

Here we aim at establishing certain new fractional integral inequalities involving the Gauss hypergeometric function for synchronous functions which are related to the Chebyshev functional. Several special cases as fractional integral inequalities involving Saigo, Erdélyi-Kober, and Riemann-Liouville type fractional integral operators are presented in the concluding section. Further, we also consider their relevance with other related known results.

scholarly journals On weighted inequalities for certain fractional integral operators

2006 ◽  
Vol 2006 ◽  
pp. 1-7
Author(s):  
R. K. Raina
Keyword(s):  
Hypergeometric Function ◽  
Fractional Integral ◽  
Integral Operators ◽  
Gauss Hypergeometric Function ◽  
Weighted Inequalities ◽  
Fractional Integral Operators

This paper considers the modified fractional integral operators involving the Gauss hypergeometric function and obtains weighted inequalities for these operators. Multidimensional fractional integral operators involving the H-function are also introduced.

Fractional operators in the matrix variate case

2013 ◽  
Vol 16 (2) ◽  
Author(s):  
A. Mathai ◽  
Hans Haubold
Keyword(s):  
Hypergeometric Function ◽  
Fractional Integral ◽  
Integral Operators ◽  
Natural Sciences ◽  
Gauss Hypergeometric Function ◽  
Fractional Operators ◽  
Fractional Integral Operators ◽  
The Matrix ◽  
Functional Forms ◽  
The Ideal

AbstractFractional integral operators connected with real-valued scalar functions of matrix argument are applied in various problems of mathematics, statistics and natural sciences. In this survey we start with considering the case of a Gauss hypergeometric function with the argument being a rectangular matrix. Subsequently, some fractional integral operators are introduced which complement theresults available on fractional operators in the matrix variate cases. Several properties and limiting forms are derived. Then the pathway idea is incorporated to move among several different functional forms. When these are used as models for problems in the natural sciences, then these can cover the ideal situations, neighborhoods, in between stages and paths leading to optimal situations.

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 On certain new CAUCHY–TYPE fracitioanl integral inequalities and OPIAL–TYPE fractional derivative inequalities

2015 ◽  
Vol 46 (1) ◽  
pp. 67-73 ◽  
Author(s):  
Amit Chouhan
Keyword(s):  
Fractional Derivative ◽  
Fractional Integral ◽  
Integral Operators ◽  
Integral Inequalities ◽  
Future Research ◽  
Cauchy Type ◽  
Fractional Integral Operators ◽  
Integrable Functions ◽  
New Inequalities

The aim of this paper is to establish several new fractional integral and derivative inequalities for non-negative and integrable functions. These inequalities related to the extension of general Cauchy type inequalities and involving Saigo, Riemann-Louville type fractional integral operators together with multiple Erdelyi-Kober operator. Furthermore the Opial-type fractional derivative inequality involving H-function is also established. The generosity of H-function could leads to several new inequalities that are of great interest of future research.

scholarly journals Inequalities by Means of Generalized Proportional Fractional Integral Operators with Respect to Another Function

Mathematics ◽  
2019 ◽  
Vol 7 (12) ◽  
pp. 1225 ◽  
Author(s):  
Saima Rashid ◽  
Fahd Jarad ◽  
Muhammad Aslam Noor ◽  
Humaira Kalsoom ◽  
Yu-Ming Chu
Keyword(s):  
Real World ◽  
Fractional Integral ◽  
Numerical Approximation ◽  
Integral Operators ◽  
Integral Inequalities ◽  
The Novel ◽  
Fractional Integral Operators ◽  
Real World Problems

In this article, we define a new fractional technique which is known as generalized proportional fractional (GPF) integral in the sense of another function Ψ . The authors prove several inequalities for newly defined GPF-integral with respect to another function Ψ . Our consequences will give noted outcomes for a suitable variation to the GPF-integral in the sense of another function Ψ and the proportionality index ς . Furthermore, we present the application of the novel operator with several integral inequalities. A few new properties are exhibited, and the numerical approximation of these new operators is introduced with certain utilities to real-world problems.

scholarly journals On new general versions of Hermite–Hadamard type integral inequalities via fractional integral operators with Mittag-Leffler kernel

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Havva Kavurmacı Önalan ◽  
Ahmet Ocak Akdemir ◽  
Merve Avcı Ardıç ◽  
Dumitru Baleanu
Keyword(s):  
Integral Equation ◽  
Fractional Integral ◽  
Integral Operators ◽  
Integral Inequalities ◽  
Fractional Integral Operators ◽  
Frequency Of Use ◽  
Second Derivatives ◽  
New Variant ◽  
Type Integral ◽  
Basic Concepts

AbstractThe main motivation of this study is to bring together the field of inequalities with fractional integral operators, which are the focus of attention among fractional integral operators with their features and frequency of use. For this purpose, after introducing some basic concepts, a new variant of Hermite–Hadamard (HH-) inequality is obtained for s-convex functions in the second sense. Then, an integral equation, which is important for the main findings, is proved. With the help of this integral equation that includes fractional integral operators with Mittag-Leffler kernel, many HH-type integral inequalities are derived for the functions whose absolute values of the second derivatives are s-convex and s-concave. Some classical inequalities and hypothesis conditions, such as Hölder’s inequality and Young’s inequality, are taken into account in the proof of the findings.

scholarly journals Certain parameterized inequalities arising from fractional integral operators with exponential kernels

Filomat ◽  
2021 ◽  
Vol 35 (5) ◽  
pp. 1707-1724
Author(s):  
Zhengrong Yuan ◽  
Taichun Zhou ◽  
Qiang Zhang ◽  
Tingsong Du
Keyword(s):  
Distribution Function ◽  
Cumulative Distribution Function ◽  
Fractional Integral ◽  
Integral Operators ◽  
Integral Inequalities ◽  
Cumulative Distribution ◽  
Digamma Function ◽  
Fractional Integral Operators ◽  
Definition Of ◽  
Fractional Type

We utilize the definition of a fractional integral operators, which was presented by Ahmad et al., to investigate a general fractional-type identity with a parameter. We establish certain parameterized fractional integral inequalities based on this identity, and provide two examples to illustrate the obtained results. Also, these results derived in this paper are applied to the estimations of q-digamma function, divergence measures and cumulative distribution function, respectively.

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