On <i>ν</i>-Level Interval of Fuzzy Set for Fractional Order Neutral Impulsive Stochastic Differential System

Abstract

The main concern of this paper is to investigate the existence and uniqueness of a fuzzy neutral impulsive stochastic differential system with Caputo fractional order driven by fuzzy Brownian motion using fuzzy numbers with bounded ν-level intervals that are convex, normal and upper-semicontinuous. Fuzzy Itô process, Grönwall’s inequality and the Banach fixed-point theorem are employed to probe the local and global existence. An analytical example is provided to examine the theoretical results.

Keywords

• fuzzy stochastic differential equation
• fuzzy Itô process
• neutral impulsive system
• Caputo fractional derivative
• Banach fixed-point theorem