Existence and controllability results for integrodifferential equations with state-dependent delay and random effects

Abstract

The goal of this study is to investigate the existence and uniqueness of mild solutions, as well as controllability outcomes, for random integrodifferential equations with state-dependent delay. We prove the existence and uniqueness of mild solutions in the case where the nonlinear term is of the Carath?odory type and meets various weakly compactness conditions. Our research is based on Dardo?s fixed point theorem, M?nch?s fixed point theorem, a random fixed point with a stochastic domain, and Grimmer?s resolvent operator theory. Finally, an example is provided to demonstrate the outcomes that were obtained.

Controllability of integrodifferential equations with state-dependent Delay

“…Jothimani et al [24] examined the controllability of nondensely fractional neutral delay differential equation under the hille-Yosida conditon in Banach space by using Schauder fixed point theorem and semigroup theory. Recently, Diop et al [14] investigated the existence and controllability results for a class of integrodifferential equations with SDD and random effects. The authors established sufficient conditions for the controllability of the system by employing the fixed point technique and Grimmer's resolvent operator theory.…”

New discussion on global existence and attractivity of mild solutions for nonautonomous integrodifferential equations with state-dependent delay

“…However, complicated situations in which the delay depends on unknown functions have been considered in recent years. These equations are frequently called equations with state-dependent delay, see, for instance, [13,15]. Moreover, state-dependent delays are more prevalent and adequate in applications, some nice examples of state-dependent delay models are presented in [1,7] and the references therein.…”

“…Fall et al [15] established the existence of mild solutions for a class of impulsive integrodifferential equations with state-dependent delay. Diop et al [13] considered the existence and uniqueness of mild solutions, as well as controllability outcomes, for random integrodifferential equations with state-dependent.…”