Abstract
By virtue of fractional integral identities, incomplete beta function, useful series, and inequalities, we apply the concept of GG-convex function to derive new type Hermite-Hadamard inequalities involving Hadamard fractional integrals. Finally, some applications to special means of real numbers are demonstrated.
Highlights
Fractional calculus played an important role in various fields such as electricity, biology, economics, and signal and image processing [1,2,3,4,5,6,7,8]
The fractional Hermite-Hadamard inequality gives a lower and an upper estimation for both righthand and left-hand integrals average of any convex function defined on a compact interval, involving the midpoint and the endpoints of the domain
Our group go on studying fractional version Hermite-Hadamard inequality involving Riemann-Liouville and Hadamard fractional integrals for all kinds of functions [11,12,13,14,15,16,17,18,19]
Summary
Fractional calculus played an important role in various fields such as electricity, biology, economics, and signal and image processing [1,2,3,4,5,6,7,8]. Set [9] firstly studied fractional Ostrowski inequalities involving Riemann-Liouville fractional integrals. Sarikaya et al [10] studied Hermite-Hadamard type inequalities involving Riemann-Liouville fractional integrals. Our group go on studying fractional version Hermite-Hadamard inequality involving Riemann-Liouville and Hadamard fractional integrals for all kinds of functions [11,12,13,14,15,16,17,18,19]. In the forthcoming works, we will try to extend to study fractional version Hermite-Hadamard inequalities in n variables based on such fundamental results. We will use the above concepts and lemmas to derive some new fractional Hermite-Hadamard inequalities involving Hadamard fractional integrals
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