Initial value problems for nonlinear fractional equations
with discontinuous sources

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.