Abstract
Recently, many fractional integral operators were introduced by different mathematicians. One of these fractional operators, Atangana-Baleanu fractional integral operator, was defined by Atangana and Baleanu (Atangana and Baleanu, 2016). In this study, firstly, a new identity by using Atangana-Baleanu fractional integral operators is proved. Then, new fractional integral inequalities have been obtained for convex and concave functions with the help of this identity and some certain integral inequalities.
Highlights
Mathematics is a tool that serves pure and applied sciences with its deep-rooted history as old as human history and sheds light on how to express and solve problems
By defining spaces and algebraic structures built on spaces, mathematics creates structures that contribute to human life and nature
The concept of function is one of the basic structures of mathematics, and many researchers have focused on new function classes and made efforts to classify the space of functions
Summary
Mathematics is a tool that serves pure and applied sciences with its deep-rooted history as old as human history and sheds light on how to express and solve problems. In the sequel of this paper, we will denote the normalization function with BðαÞ with the same properties with the MðαÞ which is defined in Caputo-Fabrizio definition. The associated fractional integral operator has been defined by Atangana-Baleanu as follows. In [17], Akdemir et al have presented some new variants of celebrated Chebyshev inequality via generalized fractional integral operators.
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