Some Remarks on Local Fractional Integral Inequalities Involving Mittag–Leffler Kernel Using Generalized ( E, h )-Convexity

Wedad Saleh, Abdelghani Lakhdari, Ohud Almutairi and Adem Kiliçman ()
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Wedad Saleh: Department of Mathematics, Taibah University, Al-Medina 42353, Saudi Arabia
Abdelghani Lakhdari: Department CPST, Ecole Nationale Supérieure de Technologie et d’Ingénierie, Annaba 23005, Algeria
Ohud Almutairi: Department of Mathematics, University of Hafr Al-Batin, Hafr Al-Batin 31991, Saudi Arabia
Adem Kiliçman: Department of Mathematics and Statistics, Universiti Putra Malaysia (UPM), Serdang 43400, Malaysia

Mathematics, 2023, vol. 11, issue 6, 1-13

Abstract: In the present work, we introduce two new local fractional integral operators involving Mittag–Leffler kernel on Yang’s fractal sets. Then, we study the related generalized Hermite–Hadamard-type inequality using generalized ( E , h ) -convexity and obtain two identities pertaining to these operators, and the respective first- and second-order derivatives are given. In terms of applications, we provide some new generalized trapezoid-type inequalities for generalized ( E , h )-convex functions. Finally, some special cases are deduced for different values of δ , E , and h .

Keywords: fractal sets; generalized ( E , h )-convexity; local fractional integral and derivative; generalized Mittag–Leffler function (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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