Stability analysis of neutral linear fractional system with distributed delays

Veselinova, Magdalena; Kiskinov, Hristo; Zahariev, Andrey

doi:10.2298/fil1603841v

Cited by 15 publications

(21 citation statements)

References 7 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…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].…”

mentioning

confidence: 99%

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

et al. 2020

View full text Add to dashboard Cite

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].

show abstract

mentioning

confidence: 99%

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

et al. 2020

View full text Add to dashboard Cite

show abstract

“…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%

“…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%

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.

View full text Add to dashboard Cite

show abstract

“…For such equations and systems, existence and uniqueness of solutions, and stability analysis were established. 17,21,22 In this paper, we propose a new model of the fractional Black-Scholes equation by using the right fractional derivatives to model the terminal value problem. The pricing of options is a backward problem, and so the option pricing at time t depends on the terminal value at time T. The right fractional derivatives of a function f(t) is determined by the value of the future of f(t).…”

Section: Introductionmentioning

confidence: 99%

Fractional model and solution for the Black‐Scholes equation

Duan

Lü

Chen

et al. 2017

Math Methods in App Sciences

View full text Add to dashboard Cite

This work presents a new model of the fractional Black-Scholes equation by using the right fractional derivatives to model the terminal value problem. Through nondimensionalization and variable replacements, we convert the terminal value problem into an initial value problem for a fractional convection diffusion equation. Then the problem is solved by using the Fourier-Laplace transform. The fundamental solutions of the derived initial value problem are given and simulated and display a slow anomalous diffusion in the fractional case. KEYWORDS asset pricing models, Black-Scholes equation, fractional derivative, initial value problem, mathematical finance, terminal value problem Math Meth Appl Sci. 2018;41 697-704.wileyonlinelibrary.com/journal/mma

show abstract

Stability analysis of neutral linear fractional system with distributed delays

Cited by 15 publications

References 7 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

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

Fractional model and solution for the Black‐Scholes equation

Contact Info

Product

Resources

About