Inequalities for new class of fractional integral operators

Volume 10, Issue 12, pp 6166--6176 http://dx.doi.org/10.22436/jnsa.010.12.04

Publication Date: December 02, 2017 Submission Date: September 27, 2017

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Authors

Hasib Khan - College of Engineering, Mechanics and Materials, Hohai University, 211100, Nanjing, P. R. China. - Department of Mathematics, Shaheed Benazir Bhutto University Sheringal, Dir Upper, 18000, Khyber Pakhtunkhwa, Pakistan. Hongguang Sun - College of Engineering, Mechanics and Materials, Hohai University, 211100, Nanjing, P. R. China. Wen Chen - College of Engineering, Mechanics and Materials, Hohai University, 211100, Nanjing, P. R. China. Dumitru Baleanu - College of Engineering, Mechanics and Materials, Hohai University, 211100, Nanjing, P. R. China. - Department of Mathematics, Cankaya University, 06530 Ankara, Turkey. - Institute of Space Sciences, P. O. BOX, MG-23, 76900 Magrrele-Bucharest, Romania.

Abstract

The applications of fractional order integrals have promoted the study of inequalities. In this paper, we utilize recently introduced left- and right-fractional conformable integrals (FCI) for a class of decreasing \(n\) positive functions such that \(n\in N\), for the generalization of existing integral inequalities. Our results have the potentials to be used for the investigation of positive solutions of different classes of fractional differential equations.

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Keywords

• Fractional integral inequalities
• left-fractional conformable integral
• right-fractional conformable integral

MSC

•  26D10
•  26A33

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