Optimal Control Results for Sobolev-Type Fractional Stochastic Volterra-Fredholm Integrodifferential Systems of Order ϑ ∈ (1, 2) via Sectorial Operators

An analysis on the approximate controllability outcomes for fractional stochastic Sobolev‐type hemivariational inequalities of order 1 < r < 2 using sectorial operators

“…These equations have applications in various fields, including physics, engineering, and biology. Many researchers have studied controllability analysis of fractional order by employing the Sobolev-type equation [17,24,27,28].…”

“…In recent times, significant attention has been devoted to studying the controllability, existence, stability, uniqueness, and other qualitative and quantitative properties of solutions to stochastic evolution equations or inclusion problems. This growing interest can be observed through research papers such as [22–26], as well as the references cited therein. These works contribute to the exploration and understanding of the aforementioned properties in the context of stochastic systems.…”

“…He et al [30] proved the existence of mild solutions for nonlocal fractional evolution inclusions of order $$$ \alpha \in \left(1,2\right) $$$ by using the concepts of fractional calculus, multivalued analysis, the cosine family, method of measure of noncompactness, and fixed‐point theorem. Inspired by these articles, very recently, in [4, 15, 20, 23, 24, 31], the authors discussed the existence, controllability, and approximate controllability of the fractional evolution systems of order $$$ 1&amp;lt;r&amp;lt;2 $$$ with or without delay by using the concepts of fractional calculus, multivalued analysis, the cosine family, method of measure of noncompactness, and fixed‐point theorems.…”

New discussion on optimal feedback control for Caputo fractional neutral evolution systems governed by hemivariational inequalities

“…In previous research [28,29], optimal control results for both hyperbolic and antiperiodic quasilinear hemivariational inequalities were incorporated. In earlier studies [30][31][32][33][34][35], the authors presented optimal control results for the various systems.…”

Sobolev‐type existence results for impulsive nonlocal fractional stochastic integrodifferential inclusions of order ϱ∈(1,2) with infinite delay via sectorial operator

“…Very recently, Mohan Raja et al [50–52] have developed the existence, optimal controls, and approximate controllability results for fractional derivatives of order $$$ r\in \left(1,2\right) $$$ by utilizing the sectorial operators, integrodifferential systems, multivalued functions, and various fixed point techniques. Johnson et al [53, 54] discussed the effectiveness of optimal controllability in fractional order $$$ r\in \left(1,2\right) $$$ by utilizing sectorial operators, stochastic systems, impulsive conditions, and fixed point approaches. However, these results only pay attention to the controllability results for a class of fractional system of order $$$ r\in \left(1,2\right) $$$ via sectorial operator without impulsive effect, which is the main motivation to consider no work has been reported in the literature about the existence of Sobolev‐type fractional stochastic impulsive Volterra–Fredholm integro differential system of order $$$ r\in \left(1,2\right) $$$ on the sectorial operator.…”