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Certain Chebyshev-Type Inequalities Involving Fractional Conformable Integral Operators

1
Department of Mathematics, Shaheed Benazir Bhutto University, Sharingal, Upper Dir, Khyber Pakhtoon Khwa 18000, Pakistan
2
Department of Mathematics, University of Education Lahore, Dera Ghazi Khan Campus 54770, Pakistan
3
Department of Mathematics, Shaheed Benazir Bhutto University, Sharingal, Upper Dir, Khyber Pakhtoon Khwa 18000, Pakistan
4
Faculty of Science and Arts, Department of Mathematics, Ordu University, Ordu 52000, Turkey
5
Department of Mathematics, College of Arts and Sciences, Prince Sattam Bin Abdulaziz University, Wadi Aldawaser 11991, Saudi Arabia
*
Author to whom correspondence should be addressed.
Mathematics 2019, 7(4), 364; https://doi.org/10.3390/math7040364
Received: 2 April 2019 / Revised: 15 April 2019 / Accepted: 16 April 2019 / Published: 21 April 2019
(This article belongs to the Special Issue Special Functions and Applications)
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PDF [749 KB, uploaded 25 April 2019]

Abstract

Since an interesting functional by P.L. Chebyshev was presented in the year 1882, many results, which are called Chebyshev-type inequalities, have been established. Some of these inequalities were obtained by using fractional integral operators. Very recently, a new variant of the fractional conformable integral operator was introduced by Jarad et al. Motivated by this operator, we aim at establishing novel inequalities for a class of differentiable functions, which are associated with Chebyshev’s functional, by employing a fractional conformable integral operator. We also aim at showing important connections of the results here with those including Riemann–Liouville fractional and classical integrals. View Full-Text
Keywords: Riemann–Liouville (R-L) fractional integral; fractional conformable integral; Chebyshev’s functional; differentiable functions; integral inequalities Riemann–Liouville (R-L) fractional integral; fractional conformable integral; Chebyshev’s functional; differentiable functions; integral inequalities
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited (CC BY 4.0).
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Rahman, G.; Ullah, Z.; Khan, A.; Set, E.; Nisar, K.S. Certain Chebyshev-Type Inequalities Involving Fractional Conformable Integral Operators. Mathematics 2019, 7, 364.

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