Existence results for a class of impulsive neutral fractional stochastic integro-differential systems with state dependent delay

Qualitative Behaviour of Stochastic Integro-differential Equations with Random Impulses

“…Furthermore, due to a combination of uncertainty and complexity, mathematical models cannot ignore the stochastic aspects since real-world systems and natural phenomena are almost always affected by stochastic disturbances. For elementary study of stochastic differential equations (SDEs) reader may refer to [4][5][6][7][8][9][10][11][12][13][14]. (Partial) differential equations driven by stochastic processes or equations with random impulses give a natural and useful way to describe a variety of impulsive occurrences in order to take them into consideration.…”

𝒮‐asymptotically 𝓌‐periodic mild solutions for noninstantaneous impulsive integro‐differential equations with state‐dependent delay

“…Differential equations with state-dependent delay have gained more and more attention because of its wide applications, and its qualitative theory is different from equations with discrete and time-dependent delays. In recent years, the research on semilinear differential or integro-differential systems with delay is becoming more and more active; see, for instance, earlier studies [18][19][20][21][22][23][24][25][26]. Suganya et al [18] took an impulsive fractional integro-differential equation in neutral form with noninstantaneous impulses and state-dependent delay into consideration; they got the existence results through the fixed point theorem and the measure of noncompactness.…”

Trotter-Kato Approximations of Impulsive Neutral SPDEs in Hilbert Spaces

“…Anguraj and Vinodkumar [2] studied the existence, uniqueness and stability results of other form of impulsive stochastic semilinear neutral functional differential equations with infinite delays. Chaudhary and Pandey [4] considered the existence of mild solutions of the impulsive neutral fractional stochastic integro-differential systems with state dependent delay. In addition, Deng, Shu and Mao [6] established a new impulsiveintegral inequality to prove the exponential stability of mild solutions for a class of impulsive neutral SPDEs driven by fBm with noncompact semigroup.…”