Stability analysis of linear fractional differential system with distributed
          delays

Veselinova, Magdalena; Kiskinov, Hristo; Zahariev, Andrey

doi:10.1063/1.4936720

Cited by 17 publications

(24 citation statements)

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“…Regarding works concerning fractional differential systems with constant delays, we point out [10][11][12][13]. Concerning the retarded differential systems with variable or distributed delays-fundamental theory and application (stability properties)-we refer to [11,[14][15][16][17][18]. Neutral fractional systems with distributed delays are essentially studied less (see [19][20][21]).…”

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confidence: 99%

Integral Representation for the Solutions of Autonomous Linear Neutral Fractional Systems with Distributed Delay

et al. 2020

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The aim of this work is to obtain an integral representation formula for the solutions of initial value problems for autonomous linear fractional neutral systems with Caputo type derivatives and distributed delays. The results obtained improve and extend the corresponding results in the particular case of fractional systems with constant delays and will be a useful tool for studying different kinds of stability properties. The proposed results coincide with the corresponding ones for first order neutral linear differential systems with integer order derivatives. MSC: 34A08; 34A12 Introduction and NotationsFractional Calculus has a long history, but it has attracted considerable attention recently as an important tool for modeling of various real problems, such as viscoelastic systems, diffusion processes, signal and control processing, and seismic processes. Detailed information about the fractional calculus theory and its applications can be found in the monographs [1][2][3][4]. Some results for fractional linear systems with delays are in given in the book [5]. The monograph [6] is devoted to the impulsive differential and functional differential equations with fractional derivatives, as well as to some of their applications.It is well known that the study of linear fractional equations (integral representation, several types of stability, etc.) is an evergreen theme for research. Concerning these fields of fundamental and qualitative investigations for linear fractional ordinary differential equations and systems we refer to [2,4,7] and the references therein. Using the Laplace transform method, several interesting results in this direction are obtained in [8,9] as well. Regarding works concerning fractional differential systems with constant delays, we point out [10][11][12][13]. Concerning the retarded differential systems with variable or distributed delays-fundamental theory and application (stability properties)-we refer to [11,[14][15][16][17][18]. Neutral fractional systems with distributed delays are essentially studied less (see [19][20][21]). Stability properties of retarded fractional systems with derivatives of distributed order are studied in [22]. One of the existing best applications of fractional order equations with delays is modeling human manual control, in which perceptual and neuromuscular delays introduce a delay term. As interesting studies, we refer to [23,24].

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Integral Representation for the Solutions of Autonomous Linear Neutral Fractional Systems with Distributed Delay

et al. 2020

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“…The survey from Li, Zhang [7] gives a good overview of the contributions to the stability theory of fractional differential equations. Stability results are received in the noteworthy works of Deng, Li, Lu [2] and Qian, Li, Agarwal, Wong [10] for fractional system with constant delays, and in [11] for fractional system with distributed delays. It must be mentioned that the first detailed study of the linear delay differential equations and system with distributed delays (fundamental theory, stability, oscillation behavior, etc.)…”

Section: Introductionmentioning

confidence: 99%

Stability analysis of neutral linear fractional system with distributed delays

Veselinova

Kiskinov

Zahariev

2016

Filomat

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The aim of the present work is to study the initial value problem for neutral linear fractional differential system with distributed delays in incommensurate case. Furthermore, in the autonomous case with derivatives in the Riemann-Liouville or Caputo sense we establish that if all roots of the introduced characteristic equation have negative real parts, then the zero solution is globally asymptotically stable. The proposed condition coincides with the conditions which guaranty the same result in the particular case of system with constant delays. (Magdalena Veselinova), kiskinov@uni-plovdiv.bg (Hristo Kiskinov), zandrey@uni-plovdiv.bg (Andrey Zahariev)

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“…For all questions about the existing, uniqueness and continuation on R + of the solutions of the IVP problems (3.1), (3.2) and (3.1), (3.3) we refer [11], [13] and [12]. Note that in [12] is studied also when for the system (3.1) can be applied correct the Laplace transform.…”

Section: φ(T)| Is a Banach Space Of Initial Vector Functionsmentioning

confidence: 99%

“…For linear fractional system with single order derivatives and constant delays we point out the works [3] and [15]. The case of distributed delays for retarded type fractional system of is studied in [11], [14] and for neutral systems in [13] and [12]. Some stability results for fractional system with distributed order derivatives and constant delays are given in [9] and the case of distributed delays is considered in [1].…”

Section: Introductionmentioning

confidence: 99%

“…Some stability results for fractional system with distributed order derivatives and constant delays are given in [9] and the case of distributed delays is considered in [1]. The works [11] and [13] are our first motivation to extend and improve some of the obtained there explicit type sufficient conditions for asymptotical stability of the zero solution of this systems.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

A Note About Stability of Fractional Retarded Linear Systems With Distributed Delays

Milev¹,

Zlatev²

2017

Int. J. of Pure and Appl. Math.

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Stability analysis of linear fractional differential system with distributed delays

Cited by 17 publications

References 3 publications

Integral Representation for the Solutions of Autonomous Linear Neutral Fractional Systems with Distributed Delay

Integral Representation for the Solutions of Autonomous Linear Neutral Fractional Systems with Distributed Delay

Stability analysis of neutral linear fractional system with distributed delays

A Note About Stability of Fractional Retarded Linear Systems With Distributed Delays

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