On fractional differential equations and inclusions with nonlocal and average-valued (integral) boundary conditions

Abstract

This paper is concerned with the existence of solutions for boundary value problems of fractional differential equations and inclusions supplemented with nonlocal and average-valued (integral) boundary conditions. The existence results for the single-valued case (equations) are obtained by means of fixed point theorems due to O’Regan and Sadovski, whereas the existence of solutions for the multivalued case (inclusions) is established via nonlinear alternative for contractive maps. The obtained results are well illustrated by examples.