Abstract
The aim of this paper is to present the fractional Hadamard and Fejér-Hadamard inequalities for exponentially s,m-convex functions. To establish these inequalities, we will utilize generalized fractional integral operators containing the Mittag-Leffler function in their kernels via a monotone function. The presented results in particular contain a number of fractional Hadamard and Fejér-Hadamard inequalities for s-convex, m-convex, s,m-convex, exponentially convex, exponentially s-convex, and convex functions.
Highlights
Introduction and PreliminariesIntegral operators play an important role in the subject of mathematical analysis
The aim of this paper is to present the fractional Hadamard and Fejér-Hadamard inequalities for exponentially ðs, mÞ-convex functions
Fractional integral operators have been proven very useful in almost all fields of science and engineering
Summary
Integral operators play an important role in the subject of mathematical analysis. Fractional integral operators have been proven very useful in almost all fields of science and engineering. We give the definition of generalized fractional integral operators containing the Mittag-Leffler function in their kernels as follows. If we take γðuÞ = uτ in (7) and (9), we get the following generalized fractional integral operators containing the Mittag-Leffler function. The main purpose of this article is to establish the Hadamard and the Fejér-Hadamard inequalities for exponentially ðs, mÞ-convex functions by utilizing the generalized fractional integral operators (9) and (10) containing the MittagLeffler function. We will consider real parameters of the Mittag-Leffler function
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