Topological Method for Coupled Systems of Impulsive Neutral Functional Differential Inclusions Driven by a Fractional Brownian Motion and Wiener Process

Abstract

In this paper we prove the existence of mild solutions for a first-order im-
pulsive semilinear stochastic differential inclusion with an infinite-dimensional
fractional Brownian motion and a standard cylindrical Wiener process. We fo-
cus on convex-valued case. The results are obtained by using two different fixed
point theorems for multivalued mappings, more precisely, the technique is based
on multivalued version of a nonlinear alternative of Leray-Schauder’s fixed point
theorem in generalized Banach spaces.