4.6 Article

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

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Summary: This paper focuses on the existence results of the solution and the finite-time stability for fractional fuzzy differential equations involving non-instantaneous impulsive effects and perturbance parameters. The existence of a unique solution is proved using the fixed point theorem of a weakly contractive mapping on the partially ordered fuzzy space, and the sufficient condition of finite-time stability is obtained using the generalized fractional Gronwall inequality. The fuzzy fractional derivatives used in this study include the concept of derivatives based on the generalized Hukuhara difference and the granular difference. The results based on the granular difference overcome restrictions associated with previous approaches defined via the generalized Hukuhara difference concept. Numerical examples are provided to verify the main results.

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