Generalized fractional Steffensen type inequalities

Abstract

In this paper, we state, prove and discuss new general Steffensen type inequality. As a special case of that general result we obtain fractional inequalities involving fractional integrals and derivatives of Riemann-Liouville, Canavati, Caputo, Hadamard and Erdelyi-Kóber types as well as fractional integrals of a function with respect to another function. Furthermore, we show that our main result covers much more general situations applying it to multidimensional settings. Finally we give mean value theorems for linear functionals related to obtained Steffensen type inequalities.