Generalized Riemann-Liouville <inline-formula> <tex-math notation="LaTeX">$k$ </tex-math></inline-formula>-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.

Keywords

• Fractional inequalities
• Hadamard inequality
• Ostrowski inequality
• Riemann-Liouville fractional integrals
• Generalized fractional integrals