分数阶脉冲微分系统的广义Mittag-Leffler稳定性
Generalized Mittag-Leffler stability of fractional impulsive differential system
摘要：
建立了一类具有脉冲条件和脉冲点处波动下界的脉冲Hilfer分数阶微分方程的温和解的整表示.进一步，给出了一类具有Hilfer阶的脉冲分数阶微分系统广义Mittag-Leffler稳定的充分条件.分析延伸通过瞬时和非瞬时脉冲条件。该理论利用连续李雅普诺夫函数，以确定稳定性条件。给出了一个例子，研究了非瞬时脉冲条件下具有可变下界的系统的解。
英文摘要：
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.
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