Controllability of Fractional Stochastic Delay Systems Driven by the Rosenblatt Process

Controllability of Fractional Stochastic Delay Equations

0 g(s, x(s), x(s− τ(s))) (t− s)1−α dω(s), t ∈ J = [0, T ], x(t) = ψ(t), t ∈ [−r, 0], (1.1) where 0 < α ≤ 1, T > 0 and A is a linear closed operator , defined on a given Hilbert space X . It is assumed that A generates an analytic semigroup S(t), t ≥ 0. The state x(.) takes its values in the Hilbert spaceX , and the control function u(.) is in L2(J, U), the Hilbert space of admissible control fu...

Existence and Measurability of the Solution of the Stochastic Differential Equations Driven by Fractional Brownian Motion

Approximate Controllability of Fractional Order Neutral Control Systems with Delay

The investigation of the theory of fractional calculus has been started about three decades before. Fractional order nonlinear equations are abstract formulations for many problems arising in engineering, physics and many other fields in which the integer derivative with respect to time is replaced by a derivative of fractional order. In particular, the fractional calculus is used in diffusion ...

existence and measurability of the solution of the stochastic differential equations driven by fractional brownian motion

On the controllability of fractional dynamical systems

In the last three decades, interest in fractional calculus has experienced rapid growth and at present we can find many papers devoted its theoretical and application aspects (see the work of Machado et al. (2011) and the references therein). Fractional order models of real systems are often more adequate than the usually used integer order models in electrochemistry (Ichise et al., 1971), adve...