Error bounds associated with different versions of Hadamard inequalities of mid-point type

In this paper, we establish the error bounds of different versions of mid-point type inequalities. At first, we prove two identities for fractional integrals involving the extended generalized Mittag-Leffler function and generalized exponential fractional integrals, and then we establish the corresponding error bound inequalities. Furthermore, we find a generalized inequality for error bound inequalities using a generalized identity. Also, we find some inequalities which formulate all error bound inequalities for various versions of Hadamard inequality. Finally, we present some examples of the central moment of a random variable.