scholarly journals Stability analysis of neutral linear fractional system with distributed delays

Filomat ◽  
2016 ◽  
Vol 30 (3) ◽  
pp. 841-851 ◽  
Author(s):  
Magdalena Veselinova ◽  
Hristo Kiskinov ◽  
Andrey Zahariev
Keyword(s):  
Stability Analysis ◽  
Zero Solution ◽  
Distributed Delays ◽  
Asymptotically Stable ◽  
Initial Value ◽  
Globally Asymptotically Stable ◽  
Fractional Differential System ◽  
Autonomous Case ◽  
Fractional Differential ◽  
Fractional System

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.

scholarly journals Existence of Absolutely Continuous Fundamental Matrix of Linear Fractional System with Distributed Delays

Mathematics ◽  
2021 ◽  
Vol 9 (2) ◽  
pp. 150
Author(s):  
Hristo Kiskinov ◽  
Ekaterina Madamlieva ◽  
Magdalena Veselinova ◽  
Andrey Zahariev
Keyword(s):  
Integral Representation ◽  
Differential System ◽  
Fundamental Matrix ◽  
Existence And Uniqueness ◽  
Sufficient Conditions ◽  
Distributed Delays ◽  
Absolutely Continuous ◽  
Fractional Differential System ◽  
Fractional Differential ◽  
Fractional System

The goal of the present paper is to obtain sufficient conditions that guaranty the existence and uniqueness of an absolutely continuous fundamental matrix for a retarded linear fractional differential system with Caputo type derivatives and distributed delays. Some applications of the obtained result concerning the integral representation of the solutions are given too.

Stability analysis and optimal control of an epidemic model with vaccination

2015 ◽  
Vol 08 (03) ◽  
pp. 1550030 ◽  
Author(s):  
Swarnali Sharma ◽  
G. P. Samanta
Keyword(s):  
Optimal Control ◽  
Stability Analysis ◽  
Epidemic Model ◽  
Asymptotically Stable ◽  
Control Pair ◽  
Globally Asymptotically Stable ◽  
The Stability ◽  
The Cost ◽  
Objective Functional ◽  
Disease Free

In this paper, we have developed a compartment of epidemic model with vaccination. We have divided the total population into five classes, namely susceptible, exposed, infective, infective in treatment and recovered class. We have discussed about basic properties of the system and found the basic reproduction number (R0) of the system. The stability analysis of the model shows that the system is locally as well as globally asymptotically stable at disease-free equilibrium E0when R0< 1. When R0> 1 endemic equilibrium E1exists and the system becomes locally asymptotically stable at E1under some conditions. We have also discussed the epidemic model with two controls, vaccination control and treatment control. An objective functional is considered which is based on a combination of minimizing the number of exposed and infective individuals and the cost of the vaccines and drugs dose. Then an optimal control pair is obtained which minimizes the objective functional. Our numerical findings are illustrated through computer simulations using MATLAB. Epidemiological implications of our analytical findings are addressed critically.

scholarly journals On the Stability Analysis of Linear Unperturbed Non-integer Differential Systems

2021 ◽  
pp. 85-89
Author(s):  
Ubong D. Akpan
Keyword(s):  
Stability Analysis ◽  
Asymptotic Stability ◽  
Differential System ◽  
Differential Systems ◽  
Caputo Derivatives ◽  
Fractional Differential System ◽  
Fractional Differential ◽  
The Stability

In this paper, the stability of non-integer differential system is studied using Riemann-Liouville and Caputo derivatives. The stability notion for determining the stability/asymptotic stability or otherwise fractional differential system is given. Example is provided to demonstrate the effectiveness of the result.

scholarly journals Stability Analysis of a Dynamical Model for Malware Propagation with Generic Nonlinear Countermeasure and Infection Probabilities

2020 ◽  
Vol 2020 ◽  
pp. 1-7
Author(s):  
Xulong Zhang ◽  
Xiaoxia Song
Keyword(s):  
Stability Analysis ◽  
Theoretical Analysis ◽  
Dynamical Model ◽  
Practical Significance ◽  
Asymptotically Stable ◽  
Unique Equilibrium ◽  
Globally Asymptotically Stable ◽  
Effective Strategies ◽  
Malware Propagation ◽  
Theoretical Results

The dissemination of countermeasures is widely recognized as one of the most effective strategies of inhibiting malware propagation, and the study of general countermeasure and infection has an important and practical significance. On this point, a dynamical model incorporating generic nonlinear countermeasure and infection probabilities is proposed. Theoretical analysis shows that the model has a unique equilibrium which is globally asymptotically stable. Accordingly, a real network based on the model assumptions is constructed, and some numerical simulations are conducted on it. Simulations not only illustrate theoretical results but also demonstrate the reasonability of general countermeasure and infection.

Global dynamics in a heroin epidemic model with different conscious stages and two distributed delays

2019 ◽  
Vol 12 (03) ◽  
pp. 1950038 ◽  
Author(s):  
Xamxinur Abdurahman ◽  
Zhidong Teng ◽  
Ling Zhang
Keyword(s):  
Epidemic Model ◽  
Drug Users ◽  
Distributed Delays ◽  
Threshold Dynamics ◽  
Uniform Persistence ◽  
Global Dynamics ◽  
Asymptotically Stable ◽  
Globally Asymptotically Stable ◽  
Number Formula ◽  
Drug Free

A heroin epidemic model with different conscious stages and distributed delays is constructed. The model allows for conscious drug users and unconscious drug users. The threshold dynamics of the model is established. It is shown that drug-free equilibrium is globally asymptotically stable when basic reproduction number [Formula: see text]; when [Formula: see text], the uniform persistence of the model is proved, and it is proved that the endemic equilibrium is globally asymptotically stable.

Global stability analysis of a fractional differential system in hepatitis B

2021 ◽  
Vol 143 ◽  
pp. 110619
Author(s):  
Lislaine Cristina Cardoso ◽  
Rubens Figueiredo Camargo ◽  
Fernando Luiz Pio dos Santos ◽  
José Paulo Carvalho Dos Santos
Keyword(s):  
Stability Analysis ◽  
Hepatitis B ◽  
Global Stability ◽  
Differential System ◽  
Global Stability Analysis ◽  
Fractional Differential System ◽  
Fractional Differential

scholarly journals Addendum to stability analysis of neutral linear fractional system with distributed delays (Filomat 30:3 (2016), 841-851)

Filomat ◽  
2017 ◽  
Vol 31 (15) ◽  
pp. 5013-5017
Author(s):  
Magdalena Veselinova ◽  
Hristo Kiskinov ◽  
Andrey Zahariev
Keyword(s):  
Fractional Integral ◽  
Initial Conditions ◽  
Initial Condition ◽  
Initial Value ◽  
Short Article ◽  
Delayed Argument ◽  
Fractional Differential ◽  
Fractional System ◽  
The Right ◽  
Equations With Delay

In this short article we discuss the initial condition of the initial value problem for fractional differential equations with delayed argument and derivatives in Riemann-Liouville sense. We provide also a new lemma - a ?mirror? analogue of the Kilbas Lemma, concerning the right side Riemann-Liouville fractional integral, which is important for the correct setting of the initial conditions, especially in the case of equations with delay.

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