Results on the approximate controllability of Atangana-Baleanu fractional stochastic delay integrodifferential systems

Backward Stackelberg Games with Delay and Related Forward–Backward Stochastic Differential Equations

“…On the other hand, controlled systems with delay have also received significant attention due to the path-dependence of the state and the time lag between the input and output (see [12][13][14][15][16]). Compared with the system driven by the Wiener process or the non-Gaussian process such as Rosenblatt process, the references [17][18][19][20][21] discussed Stackelberg games with different delays which are based on the system driven by a standard Brownian motion.…”

“…Theorem 4. Under assumption (H5), the leader's optimal control problem (LQBSG) l can be uniquely solvable if and only if there exists a unique (y * (t), z * (t), x * (t), p * (t), q * (t), ξ * (t), w * (t)) satisfying Equation (16) and Equation (17)…”

New exploration on approximate controllability of fractional neutral‐type delay stochastic differential inclusions with non‐instantaneous impulse

“…Controllability is the qualitative property of the dynamical control system which shows the existence of a control function which can steer the dynamical system from an initial state to any desired final state. In recent years, many researchers have extensively investigated controllability results for various dynamical systems [4,8,[12][13][14][15][16]. Furthermore, the deterministic models often experience variations that are random, or that at least look to be random due to environmental noise.…”

“…Its potential applications have gained a lot of importance. In the last few decades, the growth of science and engineering systems has considerably stimulated the employment of fractional calculus in various areas of the control theory, for example, in controllability, fault estimation, observability, observer design, stability, and stabilization [12,14,16,[20][21][22]. Fractional derivatives are divided into two major types; singular kernels such as the Riemann-Liouville and Caputo [22] and Hilfer derivatives [23] and nonsingular kernels such as the Caputo-Fabrizio [24] and the Atangana-Baleanu fractional derivatives [25].…”

“…Sadeghi et al [26] discussed a numerical technique and obtained a solution of fractional differential equations containing Atangana-Baleanu derivative through the operational matrices based on Genocchi polynomials together with the collocation points. Johnson et al [14] investigated the existence of mild solution and approximate controllability of Atangana-Baleanu fractional stochastic systems involving inclusion, integrodifferential, and infinite delay. Dineshkumar et al [13] discussed the existence of mild solution and approximate controllability of Atangana-Baleanu fractional stochastic systems of existence of mild solution and approximate controllability of fractional differential inclusions with delay.…”