  In this paper, we investigate the existence and uniqueness of solutions and
derive the Ulam--Hyers--Mittag--Leffler stability results for impulsive
implicit $\Psi$--Hilfer fractional differential equations with time delay. It
is demonstrated that the Ulam--Hyers and generalized Ulam--Hyers stability are
the specific cases of Ulam--Hyers--Mittag--Leffler stability. Extended version
of Gronwall inequality, abstract Gronwall lemma and Picard operator theory are
the primary devices in our investigation. We give an example to illustrate the
obtained results.
