Mathematical analysis demonstrates the existence, uniqueness, and finite-time stability of mixed Caputo fractional delay systems, highlighting new frameworks for complex memory dynamics.
Key Points
To analyze the qualitative behavior, existence, uniqueness, and finite-time stability of mixed integral Caputo fractional delay dynamic systems affected by non-instantaneous impulses.
Formulated a model incorporating neutral terms, time-dependent delays in integral bounds, and non-instantaneous impulsive actions.
Derived analytical conditions using fixed point theorems, Gronwall-type inequalities, and Hölder's inequality.
Introduced a delayed Mittag–Leffler type matrix to encapsulate dynamic memory and time-lag effects, verified via a numerical example.
Established sufficient criteria guaranteeing the existence and uniqueness of solutions across the specified fractional delay framework.
Formulated analytical bounds ensuring the finite-time stability of the system under non-instantaneous impulsive perturbations.