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We consider the periodic boundary value problem (PBVP) for a semilinear fractional-order delayed functional differential inclusion in a Banach space. We introduce and study a multivalued integral operator whose fixed points coincide with mild solutions of our problem. On that base, we prove the main existence result (Theorem ). We present an example dealing with existence of a trajectory for a time-fractional diffusion type feedback control system with a delay satisfying periodic boundary value condition.

In this paper we consider a nonlinear control system affected by deterministic uncertainty and described by a system of ordinary differential equations. The uncertainty is modelled by a multivalued map whose t-measurable and x-Lipschitz selections represent the possible system dynamics of the uncertain system. We propose a dynamical feedback control design, based on the singular perturbation theory, which allows all the possible system trajectories corresponding to the system dynamics to have the same prescribed behaviour. Specifically, given a manifold K of the state space, defined as the zeros of a smooth map, the proposed control steers and then holds, during finite or infinite time intervals, any possible system trajectory to any prescribed neighbourhood of K. A result ensuring the exact attainability of K is also provided. Some examples illustrating the obtained results are presented.

We combine the methods of the topological degree with techniques developed by J. K. Hale and G. Raugel to study the periodic solutions of a damped nonlinear hyperbolic equation in a thin domain. Academic Press