Abstract
In this paper, we study the controllability for a system governed by fractional non-instantaneous non-linear impulsive differential inclusions in Banach spaces. We adopt a new approach to derive the controllability results under weak conditions by establishing a new version weakly convergent criteria in the piecewise continuous functions spaces. In particular, we emphasize that we do not assume any regularity conditions on the multivalued non-linearity expressed in terms of measures of non-compactness. Moreover, unlike the previous literatures, we also do not restrict that the invertibility of the linear controllability operator satisfies a condition expressed in terms of measures of non-compactness. It allows us to apply the weakly topology theory for weakly sequentially closed graph operator and to obtain the controllability results for both upper weakly sequentially closed and relatively weakly compact types of non-linearity.