Inverting of generalized Riemann–Liouville operator by means of integral Laplace transform

Abstract

We employ the integral Laplace transform to invert the generalized Riemann–Liouville operator in a closed form. We establish that the inverse generalized Riemann–Liouville operator is a differential or integral-differential operator. We establish a relation between Riemann–Liouville operator and Temlyakov–Bavrin operator. We provide new examples of generalized Riemann–Liouville operator.