Abstract
We investigate the existence and controllability of integral solutions to non-densely defined Hilfer fractional evolution equations. Our results are established by implementing the concept of a bounded integral contractor and by using a sequencing technique. In contrast to the papers available in the literature, in order to establish our exact controllability results, we do not need to define the induced inverse of the controllability operator and we do not need the non-linear function to satisfy a Lipschitz condition. We also establish trajectory controllability (which is stronger than other controllability concepts) results for Hilfer fractional evolution equations. Finally, we present and discuss an example which illustrates our results.
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