Modified Riemann–Liouville integro-differential operators in the class of harmonic functions and their applications

Abstract

In this work we study the properties of some modified integro-differential Riemann–Liouville integro-differential operators. As application of the properties of these operators we consider some local and nonlocal boundary value problems for Laplace equation in a ball. We prove existence and uniqueness for the studied problems. These problems generalize known Dirichlet and Bitsadze–Samarski problems.