Controllability of mixed Volterra–Fredholm-type integro-differential systems in Banach space

Controllability of Volterra–Fredholm type systems in Banach spaces

“…In this paper we show that the examples in [1,2] cannot be recovered as special cases of the abstract results. If the semigroup is compact, then the assumptions H2 and A2 in [1,2], respectively, are valid if and only if X is finite dimensional.…”

“…If the semigroup is compact, then the assumptions H2 and A2 in [1,2], respectively, are valid if and only if X is finite dimensional. As a result, the applications are restricted to ordinary differential control systems, see also Triggiani [7] for complementary details.…”

“…As a result, the applications are restricted to ordinary differential control systems, see also Triggiani [7] for complementary details. We remark here that there is long list of papers on exact controllability of abstract control system (including, first order systems, second order systems, abstract evolution systems and integro-differential systems) which contain a similar technical error, see for instance [1,2,[8][9][10] and the references therein. Motivated by these papers we extend the results in Triggiani [7] and Henrı´quez [4] for a class of abstract control system which will allow us to discuss the above in detail.…”

Controllability of mixed Volterra–Fredholm-type integro-differential inclusions in Banach spaces

“…Let F take its single-valued form in [10], then condition (A5) is reduced to the condition (H8) in [10]. So Theorem 3.1 gives a new sufficient condition for the controllability of the integro-differential systems by dropping assumptions (H5)-(H7) and (H9) in [10].…”

“…These problems have been extensively studied by many authors, see for instance [2][3][4][5][6][7][8][9] and the references therein. Very recently, Chalishajar [10] studied the following mixed Volterra-Fredholm-type integro-differential systems in Banach spaces:…”