Topological properties of solution sets for Sobolev-type fractional stochastic differential inclusions with Poisson jumps

Abstract

ABSTRACTIn this paper, we investigate the topological properties of solution sets for Sobolev-type fractional stochastic differential inclusions with Poisson jumps in Caputo and Riemann–Liouville fractional derivatives of order , respectively. We show that the solution set is nonempty, compact and an -set under some suitable conditions, which implies that the solution set may not be a singleton, but in 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.