Mittag-Leffler input stability of fractional differential equations and its applications

Ndolane Sene

doi:10.3934/dcdss.2020050

Article Contents

2020, Volume 13, Issue 3: 867-880. Doi: 10.3934/dcdss.2020050

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Mittag-Leffler input stability of fractional differential equations and its applications

Ndolane Sene^,

Département de Mathématiques de la Décision, Université Cheikh Anta Diop de Dakar, Laboratoire Lmdan, BP 5683 Dakar Fann, Sénégal

^* Corresponding author: Ndolane Sene
^* Corresponding author: Ndolane Sene

Received: July 31, 2018

Revised: September 30, 2018

Published: December 2019

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Abstract

This paper addresses the Mittag-Leffler input stability of the fractional differential equations with exogenous inputs. We continuous the first note. We discuss three properties of the Mittag-Leffler input stability: converging-input converging-state, bounded-input bounded-state, and Mittag-Leffler stability of the unforced fractional differential equation. We present the Lyapunov characterization of the Mittag-Leffler input stability, and conclude by introducing the fractional input stability for delay fractional differential equations, and we provide its Lyapunov-Krasovskii characterization. Several examples are treated to highlight the Mittag-Leffler input stability.

Keywords:

Fractional derivative,
fractional differential equations with exogenous inputs,
Mittag-Leffler input stable.

Mathematics Subject Classification: Primary: 26A33, 93D05; Secondary: 93D25.

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References

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