Asymptotic Analysis of Linear and Interval Linear Fractional-Order Neutral Delay Differential Systems Described by the Caputo-Fabrizio Derivative

Ann Al Sawoor,Miloud Sadkane

doi:10.4236/am.2020.1112084

Ann Al Sawoor, Miloud Sadkane

Open Access

https://doi.org/10.4236/am.2020.1112084

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Journal: Applied mathematics	Publication Date: Jan 1, 2020
Citations: 2	License type: CC BY 4.0

Affiliation: Université de Bretagne Occidentale

Abstract

Asymptotic stability of linear and interval linear fractional-order neutral delay differential systems described by the Caputo-Fabrizio (CF) fractional derivatives is investigated. Using Laplace transform, a novel characteristic equation is derived. Stability criteria are established based on an algebraic approach and norm-based criteria are also presented. It is shown that asymptotic stability is ensured for linear fractional-order neutral delay differential systems provided that the underlying stability criterion holds for any delay parameter. In addition, sufficient conditions are derived to ensure the asymptotic stability of interval linear fractional order neutral delay differential systems. Examples are provided to illustrate the effectiveness and applicability of the theoretical results.

Highlights

Fractional calculus is attracting more and more researchers in applied sciences and engineering because of many advantages of fractional derivatives which provide important tools in modelling natural phenomena, see, e.g., [1] [2]
In [19] the authors consider the asymptotic stability for uncertain singular neutral delay systems and in [20] [21] [22] the authors study the stability analysis of interval linear fractional ordinary differential systems, interval linear fractional neutral differential systems described by the Caputo derivative and interval linear fractional neutral differential-algebraic systems described by the Caputo derivative, respectively
This paper is concerned with the asymptotic stability of linear fractional-order neutral differential delay systems described by the Caputo-Fabrizio derivative

Summary

Introduction

Fractional calculus is attracting more and more researchers in applied sciences and engineering because of many advantages of fractional derivatives which provide important tools in modelling natural phenomena, see, e.g., [1] [2]. We are interested in linear and interval linear fractional-order neutral delay differential equations described by the CF derivative. In [17] the authors study the stability analysis of linear fractional-order ordinary differential equations described by the CF derivative, whereas the authors of [18] consider the stability analysis of linear fractional-order systems with time delay, establish a characteristic equation using the Laplace transform and provide some brief sufficient stability conditions. We apply a spectrum based approach to establish asymptotic stability criteria for fractional-order neutral delay differential systems and the novelty of this work lies in the following aspects.

Problem Formulation and Notation

Main Results

Numerical Examples

Conclusion