Topological properties of solution sets of fractional stochastic evolution inclusions

Abstract

Abstract In this paper, we investigate the topological structure for the solution set of Caputo type neutral fractional stochastic evolution inclusions in Hilbert spaces. We introduce the concept of mild solutions for fractional neutral stochastic inclusions and show that the solution set is nonempty compact and R δ $R_{\delta}$ -set, which means that the solution set may not be a singleton but, from the point of view of algebraic topology, it is equivalent to a point in the sense that it has the same homology group as one-point space. Finally, we illustrate the obtained theory with the aid of an example.

Keywords

• stochastic evolution inclusions
• Brownian motion
• multimaps
• compact R δ $R_{\delta}$ -set