Approximate controllability of fractional stochastic differential equations driven by mixed fractional Brownian motion via resolvent operators

Transportation Inequalities for Neutral Stochastic Differential Equations Driven by Fractional Brownian Motion with Hurst Parameter Lesser Than 1/2

“…(2015) discussed the controllability of impulsive neutral functional SDEs, Lakhel. (2016) investigated the controllability result for neutral stochastic delay functional integro-differential equations, Tamilalagan and Balasubramanniam. (2017) studied the approximate controllability of a class of fractional stochastic differential equations driven by mixed fractional Brownian motion in Hilbert space.…”

Approximate Controllability for Functional Equations with Riemann-Liouville Derivative by Iterative and Approximate Method

“…On the other hand, the notion of controllability plays a central role in the study of the theory of control and optimization. Therefore, there are a lot of works on the controllability, approximate controllability, and optimal control of linear and nonlinear differential and integral systems in various frameworks (see [10][11][12][13][14][15][16][17][18][19][20][21][22][23][24][25][26][27][28] and references therein).…”

Controllability of nonlinear fractional order integrodifferential system with input delay

“…Fortunately, the presence of fixed‐point theories brings hope to solve these technical problems, which makes the controllability problems translate into the solution of fix points . Tamilalagan and Balasubramaniam explored the approximate controllability in Hilbert space for a class of fractional stochastic control problems utilizing Brownian motion and Schaefer's fixed‐point theorem. Vijayakumar et al addressed a class of fractional order semilinear integrodifferential inclusions by using resolvent operators and Bohnenblust‐Karlin's fixed‐point theorem.…”

“…[3][4][5][6] Fractional order differential models are more accurate than integer order models to describe the real systems, [7][8][9] since it possesses both the properties of memory and heredity. 10 In light of this, fractional differentiation equations are widely utilized in science and engineering fields, as addressed in epidemiology mechanisms, 11 viscoelasticity, 12 electronic circuit, 13 stochastic model of stock-market swings, 14 and modified bituminous binders. 15 However, the controllable qualitative analysis of the nonlinear fractional order integrodifferential systems is still an important issue to be solved urgently by scholars.…”