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In the present paper, we show that the solution set of a fractional order semilinear differential inclusion in a Banach space has the topological structure of an Rδ-set. This result allows to apply a fixed point result for condensing multimaps to the translation multioperator along the trajectories of such inclusion and to prove the existence of solutions satisfying periodic and anti-periodic boundary value conditions. An example concerning with a fractional order feedback control system is presented. [ABSTRACT FROM AUTHOR]

We are considering the Cauchy problem for a semilinear fractional differential inclusion in a Banach space. By using the fixed point theory for condensing multivalued maps, we prove the local and global theorems of the existence of mild solutions to this problem. We verify the compactness of the solutions set and its continuous dependence on parameters and initial data. We demonstrate also the application of the averaging principle to the investigation of the continuous dependence of the solutions set on a parameter in the case when the right-hand side of the inclusion is rapidly oscillating. [ABSTRACT FROM AUTHOR]

We consider a neutral type operator differential inclusion and apply the topological degree theory for condensing multivalued maps to justify the question of existence of its periodic solution. By using the averaging method, we apply the abstract result to an inclusion with a small parameter. As example, we consider a delay control system with the distributed control. [ABSTRACT FROM AUTHOR]

We consider a system of two semilinear parabolic inclusions depending on a small parameter ϵ>0 which is present both in front of the derivative in one of the two inclusions and in the nonlinear terms to model high-frequency inputs.The aim is to provide conditions in order to guarantee, for ϵ>0 sufficiently small, the existence of periodic solutions and in order to study their behaviour as ϵ tends to zero. Our assumptions permit the definition of upper semicontinuous, convex valued, compact vector operators whose fixed points represent the sought-after periodic solutions. The existence of fixed points is shown by using topological degree theory arguments. [Copyright &y& Elsevier]

We obtained results on the existence and uniqueness of a mild solution for a fractional-order semi-linear differential inclusion in a Hilbert space whose right-hand side contains an unbounded linear monotone operator and a Carathéodory-type multivalued nonlinearity satisfying some monotonicity condition in the phase variables. We used the Yosida approximations of the linear part of the inclusion, the method of a priori estimates of solutions, and the topological degree method for condensing vector fields. As an example, we considered the existence and uniqueness of a solution to the Cauchy problem for a system governed by a perturbed subdifferential inclusion of a fractional diffusion type. [ABSTRACT FROM AUTHOR]