New Chebyshev type inequalities via a general family of fractional integral operators with a modified Mittag-Leffler kernel

The main goal of this article is first to introduce a new generalization of the fractional integral operators with a certain modified Mittag-Leffler kernel and then investigate the Chebyshev inequality via this general family of fractional integral operators. We improve our results and we investigat...

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Published inAIMS mathematics Vol. 6; no. 10; pp. 11167 - 11186
Main Authors Srivastava, Hari M., Kashuri, Artion, Mohammed, Pshtiwan Othman, Alsharif, Abdullah M., Guirao, Juan L. G.
Format Journal Article
LanguageEnglish
Published AIMS Press 01.01.2021
Subjects
chebyshev inequality
fox-wright function
generalized fractional integrals
integral inequalities
modified mittag-leffler kernel
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Summary:The main goal of this article is first to introduce a new generalization of the fractional integral operators with a certain modified Mittag-Leffler kernel and then investigate the Chebyshev inequality via this general family of fractional integral operators. We improve our results and we investigate the Chebyshev inequality for more than two functions. We also derive some inequalities of this type for functions whose derivatives are bounded above and bounded below. In addition, we establish an estimate for the Chebyshev functional by using the new fractional integral operators. Finally, we find similar inequalities for some specialized fractional integrals keeping some of the earlier results in view.
ISSN:2473-6988
2473-6988
DOI:10.3934/math.2021648