On certain impulsive retrograde differential equations with integer and fractional derivatives

Abstract

In this work we will deal with some backward impulsive differential equations with local and non-local conditions in Banach spaces. We will determine sufficient conditions for the existence and stability of Ulam solutions of this type of equations, the tools used are some well-known fixed point theorems, in this case the fixed point theorems of Banach, Schaefer and Krasnoselskii, lemmas and theorems on compactness and other results of functional analysis. Key words : Backward impulsive differential equations, fractional derivative, fractional integral, local condition, non-local condition, fixed point, Ulam stability.