Global existence and stability results for mild solutions of random impulsive partial integro-differential equations

Abstract

In this paper, we discuss the global existence, uniqueness, continuous dependence and exponential stability of random impulsive partial integro-differential equations is investigated. The results are obtained by using the Leray-Schauder alternative fixed point theory and Banach Contraction Principle. Finally we give an example to illustrate our abstract results.

Caputo Fractional Differential Equations with Non-Instantaneous Random Erlang Distributed Impulses

“…The study of impulsive moments in random time is very limited. Caputo fractional differential equations with instantaneously acting impulses at random times were studied in References [24][25][26][27] but there are some inaccuracies there in the mixing properties of deterministic variables and random variables and inaccuracies in the convergence of a sequence of real numbers to a random variable. Also, the type of the random distribution of the random variables is not taken into account.…”