Controllability of fractional neutral stochastic integrodifferential inclusions of order $p \in (0,1]$ p ∈ ( 0 , 1 ] , $q \in (1,2]$ q ∈ ( 1 , 2 ] with fractional Brownian motion

New discussion about the approximate controllability of fractional stochastic differential inclusions with order 1 < r < 2

“…It has been demonstrated that stochastic frameworks come out as incredible assets with more precision in detailing and examination of an event, as populace displaying, stock costs, heat conduction in materials with memory, and so on. In last two decades, the researches on existence and controllability for the stochastic evolution equations have been attracting the attention from lots of scholars, see for instance, Ahmed et al [28][29][30], Balasubramanian et al [6], Dineshkumar et al [7,31], Mahmudov et al [23], Sathiyaraj et al [11,24,32,33], and the references therein.…”

“…In [34], Qin et al established the approximate controllability and optimal controls of fractional dynamical systems of order 1 < q < 2 by using the concepts related to sectorial operators and Krasnoselskii's fixed point theorem. In [32], Sathiyaraj et al studied the controllability of fractional neutral stochastic integrodifferential inclusions of order p ∈ (0, 1], q ∈ (1, 2] by applying the concepts related to fractional Brownian motion and Bohnenblust-Karlin's fixed point theorem. Recently, in He et al [35], Zhou and He [36], Zhou et al proved the existence and controllability of fractional differential evolution equations with order 1 < 𝛼 < 2 by using the cosine and sine function of operators and fixed point technique.…”

Mean square exponential stabilization of uncertain time‐delay stochastic systems with fractional Brownian motion

“…Several attempts have been made to tackle the problem of finding solutions for fractional SDEs and their stability analysis 8–12 . Controllability of fractional stochastic integro‐differential systems have been discussed in References 13,14.…”

Controllability of neutral stochastic functional integro-differential equations driven by fractional brownian motion with Hurst parameter lesser than $ 1/2 $

“…However, few works consider the controllability of stochastic integro-differential equations driven by FBM. As examples, [12] discussed the controllability problem for neutral stochastic integro-differential equations governed by FBM, [20] studied the complete and approximate controllability of nonlinear fractional neutral stochastic integrodifferential inclusions with FBM and [13] obtained the controllability of impulsive neutral stochastic integro-differential systems with infinite delay driven by FBM. Notice that all these previous works consider equations driven by FBM with Hurst parameter H ∈ ( 1 2 , 1).…”

“…(i) The operator Lu : [0, T ] → X, defined by: Then, equation (20) takes the following abstract form: 20) has a resolvent operator (R(t)) t≥0 on X. Besides, the continuity off andĝ and assumption (ii) it ensues that f and g are continuous.…”