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

Saima Rashid, Fahd Jarad, Muhammad Aslam Noor, Humaira Kalsoom and Yu-Ming Chu
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Saima Rashid: Department of Mathematics, Government College University, Faisalabad 38000, Pakistan
Fahd Jarad: Department of Mathematics, Cankaya University, 06790 Ankara, Turkey
Muhammad Aslam Noor: Department of Mathematics, COMSATS University Islamabad, Islamabad 45550, Pakistan
Humaira Kalsoom: School of Mathematical Sciences, Zhejiang Universoty, Hangzhou 310027, China
Yu-Ming Chu: Department of Mathematics, Huzhou University, Huzhou 313000, China

Mathematics, 2019, vol. 7, issue 12, 1-18

Abstract: 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.

Keywords: Grüss inequality; generalized proportional fractional integral with respect to another function ?; integral inequalities (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2019
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