In this paper, we study the existence, uniqueness, stability through continuous dependence on initial conditions and Hyers-Ulam-Rassias stability results for random impulsive fractional pantograph differential systems by relaxing the linear growth conditions. Finally examples are given to illustrate the applications of the abstract results.

Abstract:In this paper, we study the problem of controllability of impulsive neutral evolution integro-differential equations with state-dependent delay in Banach spaces. The main results are completely new and are obtained by using Sadovskii's fixed point theorem, theory of resolvent operators, and an abstract phase space. An example is given to illustrate the theory.

No abstract

In this paper, we show the existence of mild solutions to a nonlocal problem of impulsive integrodifferential equations via a measure of noncompactness in a Banach space. Our work is based on a new fixed point theorem and it generalizes some existing results on the topic in the sense that we do not require the semigroup and nonlinearity involved in the problem to be compact.

No abstract