A study on the mild solution of special random impulsive fractional differential equations

Abstract

In this article, we deal with mild solution of special random impulsive fractional differential equations. Initially, we present the existence of the mild solution via Leray-Schauder fixed point method. After that, we establish the exponential stability of the system. Finally, we give examples to illustrate the effectiveness of the theoretical results.

Keywords

• existence,
• leray-schauder alternative fixed point
• fractional differential equation
• random impulses
• exponential stability