Controllability results for fractional semilinear delay control systems

Abstract

In this article, we have presented the controllability relationship between the semilinear control system of fractional order (1, 2] with delay and that of the semilinear control system without delay. Suppose X and U be Hilbert spaces which are separable and Z=L2[0,b;X],Zh=L2[-h,b;X],0≤h≤b and Y= L2[0 , b; U] be the function spaces. Let the semilinear control system of fractional order with delay as CDταz(τ)=Az(τ)+Bv(τ)+g(τ,z(τ-h)),0≤τ≤b;z0(θ)=ϕ(θ),θ∈[-h,0]z′(0)=z0.where 1