Finite-time stability of fractional delay differential equations involving the generalized Caputo fractional derivative with non-instantaneous impulses

For the first time, the result on finite-time stability (FTS) for fractional delay differential equations with non-instantaneous impulses (NI-FDDEs) involving the generalized Caputo fractional derivative is presented. Based on an extensive estimation of the fractional integral inequality provided in this paper, a sufficient condition is proposed to the FTS of NI-FDDEs. Some examples are provided to illustrate our theoretical results.

Automated summary

This study presents, for the first time, the result on finite-time stability (FTS) for fractional delay differential equations with non-instantaneous impulses (NI-FDDEs) involving the generalized Caputo fractional derivative. A sufficient condition for the FTS of NI-FDDEs is proposed based on an extensive estimation of the fractional integral inequality provided in this paper. Several examples are presented to illustrate the theoretical results.