On the controllability of nonlinear fractional system with control delay

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 ...

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...

Fractional order nonlinear systems with delay in iterative learning control

Keywords: Fractional order with delay Generalized Gronwall inequality Iterative learning control a b s t r a c t In this paper, we discuss a P-type iterative learning control (ILC) scheme for a class of fractional order nonlinear systems with delay. By introducing the k-norm and using Gronwall inequality, the sufficient condition for the robust convergence of the tracking errors is obtained. Ba...

Boundary Controllability of Nonlinear Fractional Integrodifferential Systems

Controllability of nonlinear implicit fractional integrodifferential systems

Integrodifferential equations arise in many fields of science and engineering such as fluid dynamics, biological models, and chemical kinetics. A detailed investigation of integrodifferential equations and their solution via the Laplace transform method can be found in the work of Burton (1983). Recently, fractional integrodifferential equations have been used to model various physical phenomen...