Hadamard and Fejér-Hadamard inequalities for generalized $ k $-fractional integrals involving further extension of Mittag-Leffler function

In this paper, $ k $-fractional integral operators containing further extension of Mittag-Leffler function are defined firstly. Then, the first and second version of Hadamard and Fejér-Hadamard inequalities for generalized $ k $-fractional integrals are obtained. Finally, by using these generalized...

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Published inAIMS mathematics Vol. 7; no. 1; pp. 681 - 703
Main Authors Yue, Ye, Farid, Ghulam, Demirel, Ayșe Kübra, Nazeer, Waqas, Zhao, Yinghui
Format Journal Article
LanguageEnglish
Published AIMS Press 01.01.2022
Subjects
convex function
fejér-hadamard inequality
hadamard inequality
k-fractional integrals
mittag-leffler function
p-convex function
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Summary:In this paper, $ k $-fractional integral operators containing further extension of Mittag-Leffler function are defined firstly. Then, the first and second version of Hadamard and Fejér-Hadamard inequalities for generalized $ k $-fractional integrals are obtained. Finally, by using these generalized $ k $-fractional integrals containing Mittag-Leffler functions, results for $ p $-convex functions are obtained. The results for convex functions can be deduced by taking $ p = 1 $.
ISSN:2473-6988
2473-6988
DOI:10.3934/math.2022043