scholarly journals Asymptotical stability of Riemann–Liouville fractional neutral systems

2017 ◽  
Vol 69 ◽  
pp. 168-173 ◽  
Author(s):  
Song Liu ◽  
Xiang Wu ◽  
Yan-Jie Zhang ◽  
Ran Yang
Keyword(s):  
Asymptotical Stability ◽  
Neutral Systems ◽  
Fractional Neutral Systems

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

Mathematics ◽  
2020 ◽  
Vol 8 (3) ◽  
pp. 364
Author(s):  
Ekaterina Madamlieva ◽  
Mihail Konstantinov ◽  
Marian Milev ◽  
Milena Petkova
Keyword(s):  
Integral Representation ◽  
Distributed Delay ◽  
Representation Formula ◽  
Neutral Systems ◽  
Initial Value ◽  
Fractional Systems ◽  
Integral Representation Formula ◽  
Linear Differential Systems ◽  
Linear Differential ◽  
Fractional Neutral Systems

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.

scholarly journals Stability of Nonlinear Fractional Neutral Differential Difference Systems

2014 ◽  
Vol 2014 ◽  
pp. 1-8
Author(s):  
Kewei Liu ◽  
Wei Jiang
Keyword(s):  
Caputo Derivative ◽  
Neutral Systems ◽  
Difference Systems ◽  
Stability And Instability ◽  
The Stability ◽  
Conditions Of Stability ◽  
Fractional Neutral Systems

We study the stability of a class of nonlinear fractional neutral differential difference systems equipped with the Caputo derivative. We extend Lyapunov-Krasovskii theorem for the nonlinear fractional neutral systems. Conditions of stability and instability are obtained for the nonlinear fractional neutral systems.

scholarly journals Asymptotical Stability of Riemann--Liouville Nonlinear Fractional Neutral Systems with Time-Varying Delays

2021 ◽  
Author(s):  
Erdal KORKMAZ ◽  
Abdulhamit Ozdemir
Keyword(s):  
Asymptotic Stability ◽  
Optimization Problems ◽  
Time Dependent ◽  
Time Varying ◽  
Stability Of Solutions ◽  
Neutral Systems ◽  
Differential Systems ◽  
Convex Optimization Problems ◽  
The Given ◽  
Fractional Neutral Systems

In this paper, we investigate the asymptotic stability of solutions for a class of nonlinear fractional neutral differential systems with time dependent delays when the given delays are unbounded. An example is used to show the efficacy of the theorems. The LMI tool box was used to calculate the solutions to the convex optimization problems.

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