In this paper, we develop controllability findings for impulsive neutral stochastic delay partial integrodifferential equations in Hilbert spaces driven by Rosenblatt process and Lévy noise. A novel set of adequate requirements is obtained utilizing a fixed point method without imposing stringent compactness constraint on the semigroup. The observed results represent generalization continuation...

By applying the Banach fixed point theorem and using an inequality technique, we investigate a kind of random impulsive integrodifferential equations of neutral type. Some sufficient conditions, which can guarantee the existence, uniqueness, and exponential stability in mean square for such systems, are obtained. Compared with the previous works, our method is new and our results can generalize...

This paper investigates the existence of the extremal solutions to the integral boundary value problem for first-order impulsive functional integrodifferential equations with deviating arguments under the assumption of existing upper and lower solutions in the reversed order. The sufficient conditions for the existence of solutions were obtained by establishing several new comparison principles...

The theory of calculus on time scales (see [1, 2] and references cited therein) was initiated by Stefan Hilger in his Ph.D. thesis in 1990 [3] in order to unify continuous and discrete analyses, and it has a tremendous potential for applications and has recently received much attention since his foundational work. In this paper, we will study the periodic boundary value problem for the first-or...

In various real-world applications, there is a necessity given to steer processes in time. More and more it becomes acknowledged in science and engineering, that these processes exhibit discontinuities. Our paper on theory of control (especially, optimal control) and on theory of dynamical systems gives a contribution to this natural or technical fact. One of the central results of our paper is...

Abstract The purpose of this work is to investigate a novel class noninstantaneous impulsive stochastic integrodifferential equations (SIDEs) driven by Brownian motion and Rosenblatt process. We construct new set adequate assumptions for the existence uniqueness mild solutions using analysis, analytic semigroup theory, integral equation fixed point methodology. Additionally, we study asymptotic...

This paper deals with a class of integrodifferential impulsive periodic systems on Banach space. Using impulsive periodic evolution operator given by us, the T0-periodic PC-mild solution is introduced and suitable Poincaré operator is constructed. By virtue of the generalized new Gronwall lemma with impulse and B-norm, the estimate on the PC-mild solutions is derived. Showing the continuity and...