Nonlinear boundary value problems for fractional differential inclusions with Caputo-Hadamard derivatives on the half line

Abstract

The authors establish sufficient conditions for the existence of solutions to a boundary value problem for fractional differential inclusions involving the Caputo-Hadamard type derivative of order $ r \in (1, 2] $ on infinite intervals. Both cases of convex and nonconvex valued right hand sides are considered. The technique of proof involves fixed point theorems combined with a diagonalization method.