  This paper studies a nonlinear fractional implicit differential equation
(FIDE) with boundary conditions involving a HilferHadamard type fractional
derivative. We establish the equivalence between the Cauchy-type problem (FIDE)
and its mixed type integral equation through a variety of tools of some
properties of fractional calculus and weighted spaces of continuous functions.
The existence and uniqueness of solutions are obtained. Further, the Ulam-Hyers
and Ulam-Hyers-Rassias stability are discussed. The arguments in the analysis
rely on Schaefer fixed point theorem, Banach contraction principle and
generalized Gronwall inequality. At the end, an illustrative example will be
introduced to justify our results
