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

1
Department of Mathematics, Government College University, Faisalabad 38000, Pakistan
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Department of Mathematics, Cankaya University, 06790 Ankara, Turkey
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Department of Mathematics, COMSATS University Islamabad, Islamabad 45550, Pakistan
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School of Mathematical Sciences, Zhejiang Universoty, Hangzhou 310027, China
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Department of Mathematics, Huzhou University, Huzhou 313000, China
*
Author to whom correspondence should be addressed.
Mathematics 2019, 7(12), 1225; https://doi.org/10.3390/math7121225
Received: 31 October 2019 / Revised: 8 December 2019 / Accepted: 10 December 2019 / Published: 11 December 2019
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. View Full-Text
Keywords: Grüss inequality; generalized proportional fractional integral with respect to another function Ψ; integral inequalities Grüss inequality; generalized proportional fractional integral with respect to another function Ψ; integral inequalities
MDPI and ACS Style

Rashid, S.; Jarad, F.; Noor, M.A.; Kalsoom, H.; Chu, Y.-M. Inequalities by Means of Generalized Proportional Fractional Integral Operators with Respect to Another Function. Mathematics 2019, 7, 1225. https://doi.org/10.3390/math7121225

AMA Style

Rashid S, Jarad F, Noor MA, Kalsoom H, Chu Y-M. Inequalities by Means of Generalized Proportional Fractional Integral Operators with Respect to Another Function. Mathematics. 2019; 7(12):1225. https://doi.org/10.3390/math7121225

Chicago/Turabian Style

Rashid, Saima; Jarad, Fahd; Noor, Muhammad A.; Kalsoom, Humaira; Chu, Yu-Ming. 2019. "Inequalities by Means of Generalized Proportional Fractional Integral Operators with Respect to Another Function" Mathematics 7, no. 12: 1225. https://doi.org/10.3390/math7121225

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