Fractional generalized Hadamard and Fejér-Hadamard inequalities for m-convex functions

The objective of this paper is to present the fractional Hadamard and Fejér-Hadamard inequalities in generalized forms. By employing a generalized fractional integral operator containing extended generalized Mittag-Leffler function involving a monotone increasing function, we generalize the well kno...

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Published inAIMS mathematics Vol. 5; no. 6; pp. 6325 - 6340
Main Authors Yang, Xiuzhi, Farid, G., Nazeer, Waqas, Chu, Yu-Ming, Dong, Chunfa
Format Journal Article
LanguageEnglish
Published AIMS Press 01.01.2020
Subjects
extended generalized mittag-leffler function
fractional integral inequalities
generalized fractional integral operator
m-convex function
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Summary:The objective of this paper is to present the fractional Hadamard and Fejér-Hadamard inequalities in generalized forms. By employing a generalized fractional integral operator containing extended generalized Mittag-Leffler function involving a monotone increasing function, we generalize the well known fractional Hadamard and Fejér-Hadamard inequalities for m-convex functions. Also we study the error bounds of these generalized inequalities. In connection with some published results from presented inequalities are obtained.
ISSN:2473-6988
2473-6988
DOI:10.3934/math.2020407