Existence of solutions for impulsive partial stochastic neutral integrodifferential equations with state-dependent delay

Controllability of nonlocal second-order impulsive neutral stochastic functional integro-differential equations with delay and Poisson jumps

“…On the existence and the controllability for these equations, we refer the reader to (e.g. see Chang, 2007;Chang, Anguraj, & Arjunan, 2008;Karthikeyan & Balachandran, 2009Park, Balachandran, & Annapoorani, 2009;Park, Balasubramaniam, & Kumaresan, 2007;Shen & Sun, 2012;Yan & Yan, 2013, and the references therein).…”

Existence of Solutions for Fractional Partial Neutral Stochastic Functional Integro-Differential Inclusions with State-Dependent Delay and Analytic Resolvent Operators

“…Recently, Yan et al [23] studied the approximate controllability of partial fractional neutral stochastic functional integro-differential inclusions with state-dependent delay. Yan and Zhang in [25] studied the existence of mild solutions for a class of impulsive fractional partial neutral stochastic integro-differential inclusions with state-dependent delay by using properties of the solution operator and fixed point technique. Guendouzi et al [11] investigated the existence of mild solutions for a class of impulsive fractional stochastic differential inclusions with state-dependent delay in Hilbert spaces.…”

“…Sufficient conditions for the existence of solutions are derived by the authors using the nonlinear alternative of Leray-Schauder type for multivalued maps due to O'Regan. Motivated by the previously mentioned works [7,11,23,25], in this paper, we consider the existence of a class of fractional partial neutral stochastic integro-differential inclusions with state-dependent delay of the form…”

On a new class of impulsive stochastic partial neutral integro-differential equations

“…Using the Krasnoselskii-Schaefer type fixed point theorem, Hu and Ren [13] proved the existence of mild solutions for a class of impulsive neutral stochastic functional integro-differential equations with infinite delays. Yan and Yan [14] studied the existence of mild solutions for a class of impulsive partial neutral stochastic integro-differential equation with state-dependent delay. In paper [15], the authors obtained the existence and asymptotic stability of solutions to fractional impulsive neutral stochastic partial integro-differential equations with state-dependent delay.…”