  The aim of this paper is to obtain the existence of unique solution to
nonlinear Cauchy-type problem. We consider the implicit nonlinear Cauchy-type
problem with $\psi$-Hilfer fractional derivative. The Banach fixed point
theorem is used to obtain the existence of a unique solution whereas the
generalized Gronwall inequality is used to discuss continuous data dependence
of the solution. The results obtained herein are supported with illustrative
example.
