Initial value problems for nonlinear fractional equations with discontinuous sources

By Nguyen Minh Dien
DOI: 10.37550/tdmu.EJS/2022.04.357

In this paper, we consider initial value problems for nonlinear fractional equations where source functions may discontinuous. We obtain the existence and uniqueness of maximal mild solutions of the problem. We also give some appropriate conditions such that mild solutions of the problem blow-up at a finite time. Furthermore, we discuss the continuous dependence of mild solutions of the problem with respect to fractional order.