On a fractional differential inclusion involving a generalized Caputo type derivative with certain fractional integral boundary conditions

Abstract

We study a class of fractional differential inclusions defined by Caputo-Katugampola fractional derivativeinvolving a nonconvex set-valued map in the presence of certain fractional integral boundary conditions.Using a technique developed by Filippov we establish an existence result for the problem considered underthe hypothesis that the set-valued map is Lipschitz in the state variable. Also, based on a result concerningthe arcwise connectedness of the fixed point set of a class of set-valued contractions, we prove the arcwiseconnectedness of the solution set of the problem considered. The paper is the first in literature which containssuch kind of results in the framework of the problem studied.