  This paper establishes integral representations of mild solutions of
impulsive Hilfer fractional differential equations with impulsive conditions
and fluctuating lower bounds at impulsive points. Further, the paper provides
sufficient conditions for generalized Mittag-Leffler stability of a class of
impulsive fractional differential systems with Hilfer order. The analysis
extends through both, instantaneous and non-instantaneous impulsive conditions.
The theory utilizes continuous Lyapunov functions, to ascertain the stability
conditions. An example is provided to study the solution of the system with a
changeable lower bound for the non-instantaneous impulsive conditions.
