Existence theorems for mixed riemann–liouville and caputo fractional differential equations and inclusions with nonlocal fractional integro-differential boundary conditions

Abstract

In this paper, we discuss the existence and uniqueness of solutions for a new class of single and multi-valued boundary value problems involving both Riemann–Liouville and Caputo fractional derivatives, and nonlocal fractional integro-differential boundary conditions. Our results rely on modern tools of functional analysis. We also demonstrate the application of the obtained results with the aid of examples.