Explicit conditions for stability of neutral linear fractional system with distributed delays

2016 ◽  
Author(s):  
Magdalena Veselinova ◽  
Hristo Kiskinov ◽  
Andrey Zahariev
Keyword(s):  
Distributed Delays ◽  
Fractional System

scholarly journals Correction: Kiskinov et al. Existence of Absolutely Continuous Fundamental Matrix of Linear Fractional System with Distributed Delays. Mathematics 2021, 9, 150

Mathematics ◽  
2021 ◽  
Vol 9 (11) ◽  
pp. 1282
Author(s):  
Hristo Kiskinov ◽  
Ekaterina Madamlieva ◽  
Magdalena Veselinova ◽  
Andrey Zahariev
Keyword(s):  
Fundamental Matrix ◽  
Distributed Delays ◽  
Absolutely Continuous ◽  
Fractional System ◽  
The Right

We have found that, in the right side of Equation (35) in our paper [...]

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 Integral Representation of the Solutions for Neutral Linear Fractional System with Distributed Delays

2021 ◽  
Vol 5 (4) ◽  
pp. 222
Author(s):  
Hristo Kiskinov ◽  
Ekaterina Madamlieva ◽  
Magdalena Veselinova ◽  
Andrey Zahariev
Keyword(s):  
Cauchy Problem ◽  
Sufficient Conditions ◽  
Homogeneous System ◽  
Integral Representations ◽  
Distributed Delays ◽  
Inhomogeneous Systems ◽  
The Cauchy Problem ◽  
Uniqueness Of The Solution ◽  
Fractional Differential ◽  
Fractional System

In the present paper, first we obtain sufficient conditions for the existence and uniqueness of the solution of the Cauchy problem for an inhomogeneous neutral linear fractional differential system with distributed delays (even in the neutral part) and Caputo type derivatives, in the case of initial functions with first kind discontinuities. This result allows to prove that the corresponding homogeneous system possesses a fundamental matrix C(t,s) continuous in t,t∈[a,∞),a∈R. As an application, integral representations of the solutions of the Cauchy problem for the considered inhomogeneous systems are obtained.

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.

Output feedback regulation of large-scale feedforward systems with discrete and distributed delays

2021 ◽  
Vol 103 (3) ◽  
pp. 2659-2669
Author(s):  
Qingrong Liu ◽  
Hanfeng Li ◽  
Fei Zhu ◽  
Xianfu Zhang
Keyword(s):  
Output Feedback ◽  
Large Scale ◽  
Feedback Regulation ◽  
Distributed Delays

scholarly journals Differential Transform Method as an Effective Tool for Investigating Fractional Dynamical Systems

2021 ◽  
Vol 11 (15) ◽  
pp. 6955
Author(s):  
Andrzej Rysak ◽  
Magdalena Gregorczyk
Keyword(s):  
Optimal Parameter ◽  
Differential Transform Method ◽  
Bifurcation Diagrams ◽  
Transform Method ◽  
Rossler System ◽  
Differential Transform ◽  
Rössler System ◽  
Fractional System ◽  
Parameter Values

This study investigates the use of the differential transform method (DTM) for integrating the Rössler system of the fractional order. Preliminary studies of the integer-order Rössler system, with reference to other well-established integration methods, made it possible to assess the quality of the method and to determine optimal parameter values that should be used when integrating a system with different dynamic characteristics. Bifurcation diagrams obtained for the Rössler fractional system show that, compared to the RK4 scheme-based integration, the DTM results are more resistant to changes in the fractionality of the system.

Sign in / Sign up

Export Citation Format

Share Document