Generalized Riemann-Liouville $k$ -Fractional Integrals Associated With Ostrowski Type Inequalities and Error Bounds of Hadamard Inequalities

Abstract

Ostrowski inequality provides the estimation of a function to its integral mean. It is useful in error estimations of quadrature rules in numerical analysis. The objective of this paper is to define a more general form of Riemann–Liouville $k$ -fractional integrals with respect to an increasing function, which are used to obtain fractional integral inequalities of Ostrowski type. A simple and straightforward approach is followed to establish these inequalities. The applications of established results are also briefly discussed and succeeded to get bounds of some fractional Hadamard inequalities.