New Ostrowski type inequalities pertaining to conformable fractional operators

Volume 29, Issue 1, pp 28--39 http://dx.doi.org/10.22436/jmcs.029.01.03

Publication Date: August 11, 2022 Submission Date: March 28, 2022 Revision Date: May 25, 2022 Accteptance Date: June 16, 2022

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Authors

M. Tariq - Department of Basic Sciences and Related Studies, Mehran University of Engineering and Technology, Jamshoro 76062, Pakistan. S. K. Sahoo - Siksha O Anusandhan University, Bhubaneswar, , Odisha, India . H. Ahmad - Section of Mathematics, International Telematic University Uninettuno, Corso Vittorio Emanuele II, 39, 00186 Roma, Italy. A. Iampan - Department of Mathematics, School of Science, University of Phayao, Mae Ka, Mueang, Phayao 56000, Thailand. A. A. Shaikh - Department of Basic Sciences and Related Studies, Mehran University of Engineering and Technology, Jamshoro 76062, Pakistan.

Abstract

The advancements of integral inequalities with the help of fractional operators have recently been the focus of attention in the theory of inequalities. In this study, we first review some fundamental concepts, and then using \(k\)-conformable fractional integrals, we establish a new integral identity for differentiable functions. Then, considering this identity as an auxiliary result, several Ostrowski-type inequalities are presented for functions whose modulus of the first derivatives are quasi-convex. The obtained results represent generalizations as well as refinements for some published results.

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Keywords

• Ostrowski inequality
• quasi-convexity
• \(k\)-fractional conformable integral
• E-beta functions
• E-gamma functions

MSC

•  26A51
•  26A33
•  26D07
•  26D10
•  26D15

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