Generalized Mittag-Leffler stability of fractional impulsive differential system

TL;DR

This paper develops a stability analysis framework for impulsive Hilfer fractional differential systems, providing integral solution representations and stability conditions using Lyapunov functions, applicable to both instantaneous and non-instantaneous impulses.

Contribution

It introduces generalized Mittag-Leffler stability criteria for impulsive fractional systems with Hilfer order, extending stability analysis to systems with fluctuating impulsive bounds and non-instantaneous impulses.

Findings

Derived integral representations of solutions.

Established sufficient stability conditions.

Validated with an example involving variable impulsive bounds.

Abstract

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.