Certain Chebyshev-Type Inequalities Involving Fractional Conformable Integral Operators

Gauhar Rahman, Zafar Ullah, Aftab Khan, Erhan Set and Kottakkaran Sooppy Nisar
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Gauhar Rahman: Department of Mathematics, Shaheed Benazir Bhutto University, Sharingal, Upper Dir, Khyber Pakhtoon Khwa 18000, Pakistan
Zafar Ullah: Department of Mathematics, University of Education Lahore, Dera Ghazi Khan Campus 54770, Pakistan
Aftab Khan: Department of Mathematics, Shaheed Benazir Bhutto University, Sharingal, Upper Dir, Khyber Pakhtoon Khwa 18000, Pakistan
Erhan Set: Faculty of Science and Arts, Department of Mathematics, Ordu University, Ordu 52000, Turkey
Kottakkaran Sooppy Nisar: Department of Mathematics, College of Arts and Sciences, Prince Sattam Bin Abdulaziz University, Wadi Aldawaser 11991, Saudi Arabia

Mathematics, 2019, vol. 7, issue 4, 1-9

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.

Keywords: Riemann–Liouville (R-L) fractional integral; fractional conformable integral; Chebyshev’s functional; differentiable functions; integral inequalities (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2019
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (4)

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