Dynamic equations on time scales seen as generalized differential equations

Abstract

In the present paper, we prove, in the most natural framework, that dynamic equations on time scales can be treated as generalized differential equations. More precisely, we use the Henstock-Kurzweil vector integral and impose only a uniform integrability condition. Our result generalizes the main result of [24], where the embeddability of dynamic equations on time scales into generalized differential equations was proved under some assumptions of Lipschitz continuity-type (and consequently involving the Lebesgue integral).