Approximate Controllability of Non-autonomous Second Order Impulsive Functional Evolution Equations in Banach Spaces

Controllability of Impulsive Fractional Evolution Integrodifferential Equations in Banach Spaces

According to fractional calculus theory and Banach’s fixed point theorem, we establish the sufficient conditions for the controllability of impulsive fractional evolution integrodifferential equations in Banach spaces. An example is provided to illustrate the theory.

Approximate Controllability of Fractional Neutral Evolution Equations in Banach Spaces

and Applied Analysis 3 Lemma 5. The operators S α and A α have the following properties: (i) for any fixed t ≥ 0 and any x ∈ X β , one has the operators S α (t) and A α (t) which are linear and bounded operators; that is, for any x ∈ X β , 󵄩󵄩󵄩󵄩Sα (t) x 󵄩󵄩󵄩󵄩β ≤ M‖x‖β, 󵄩󵄩󵄩󵄩Aα (t) x 󵄩󵄩󵄩󵄩β ≤ M Γ (α) ‖x‖ β ; (12) (ii) the operatorsS α (t) andA α (t) are strongly continuous for all t ≥ 0; (iii) S α (...

Controllability of Impulsive Neutral Functional Differential Inclusions in Banach Spaces

and Applied Analysis 3 (A 1 ) The linear operatorW: L(J, U) → X defined by

Controllability of Second-Order Semilinear Impulsive Stochastic Neutral Functional Evolution Equations

Some Remarks on Controllability of Evolution Equations in Banach Spaces

In almost all papers in the literature, the results on exact controllability hold only for finite dimensional Banach spaces, since compactness of the semigroup and the bounded invertibility of an operator implies finite dimensional. In this note we show that the existence theory on controllability in the literature, can trivially be adjusted to include the infinite dimensional space setting, if...