  This article contains a new discussion for the generalized fractional
Cauchy-type problem involving Hilfer-Katugampola-type fractional derivative. We
study an existence and continuation of its solution. Firstly, we establish a
new theorems of local existence. Then, we deduce a continuation theorems for a
general fractional differential equations. By applying continuation theorems
deduced in this article, we present several global existence results. Moreover,
the examples are given to illustrate our main results.
