Fractional Representation Formulae Under Initial Conditions and Fractional Ostrowski Type Inequalities

Abstract

Abstract. Here we present very general fractional representation formulae for a function in terms of the fractional Riemann-Liouville integrals of different orders of the function and its ordinary derivatives under initial conditions. Based on these, we derive general fractional Ostrowski type inequalities with respect to all basic norms.

A companion of Ostrowski type integral inequality using a 5-step kernel with some applications

“…Some generalization of ostrowski type inequalities are also done in [12]- [17]. In [3], Dragomir proved the inequalities for mappings of bounded variation.…”