A comparison type theorem for linear neutral fractional systems with distributed delays

Kiskinov, Hristo; Milev, N. V.; Zahariev, Andrey

doi:10.1063/1.5013991

Cited by 5 publications

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“…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].…”

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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 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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“…Different types fractional differential equations and systems with delays (retarded and neutral) or without delays are studied for several types of stability. As works related to this theme we refer to [7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23].…”

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Asymptotic Stability of the Solutions of Neutral Linear Fractional System with Nonlinear Perturbation

Zahariev¹,

Kiskinov²

2020

Mathematics

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In this article existence and uniqueness of the solutions of the initial problem for neutral nonlinear differential system with incommensurate order fractional derivatives in Caputo sense and with piecewise continuous initial function is proved. A formula for integral presentation of the general solution of a linear autonomous neutral system with several delays is established and used for the study of the stability properties of a neutral autonomous nonlinear perturbed linear fractional differential system. Natural sufficient conditions are found to ensure that from global asymptotic stability of the zero solution of the linear part of a nonlinearly perturbed system it follows global asymptotic stability of the zero solution of the whole nonlinearly perturbed system.

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Asymptotic stability of delayed fractional system with nonlinear perturbation

Kiskinov¹,

Zahariev²

2018

AIP Conference Proceedings

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A comparison type theorem for linear neutral fractional systems with distributed delays

Cited by 5 publications

References 10 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

Asymptotic Stability of the Solutions of Neutral Linear Fractional System with Nonlinear Perturbation

Asymptotic stability of delayed fractional system with nonlinear perturbation

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