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

Abstract

We employ the integral Laplace transform to invert the generalized RiemannLiouville operator in a closed form. We establish that the inverse generalized RiemannLiouville 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.