scholarly journals On the Stability of Some Discrete Fractional Nonautonomous Systems

2012 ◽  
Vol 2012 ◽  
pp. 1-9 ◽  
Author(s):  
Fahd Jarad ◽  
Thabet Abdeljawad ◽  
Dumitru Baleanu ◽  
Kübra Biçen
Keyword(s):  
Asymptotic Stability ◽  
Global Stability ◽  
Direct Method ◽  
Uniform Stability ◽  
Lyapunov Direct Method ◽  
Uniform Asymptotic Stability ◽  
Fractional Difference ◽  
Nonautonomous Systems ◽  
The Stability

Using the Lyapunov direct method, the stability of discrete nonautonomous systems within the frame of the Caputo fractional difference is studied. The conditions for uniform stability, uniform asymptotic stability, and uniform global stability are discussed.

scholarly journals Asymptotic Stability of Distributed-Order Nonlinear Time-Varying Systems with the Prabhakar Fractional Derivatives

2020 ◽  
Vol 2020 ◽  
pp. 1-8 ◽  
Author(s):  
MohammadHossein Derakhshan ◽  
Azim Aminataei
Keyword(s):  
Asymptotic Stability ◽  
Fractional Derivatives ◽  
Direct Method ◽  
Time Varying ◽  
Lyapunov Direct Method ◽  
Fractional Differential Systems ◽  
Time Varying Systems ◽  
Fractional Differential ◽  
The Stability ◽  
Distributed Order

In this article, we survey the Lyapunov direct method for distributed-order nonlinear time-varying systems with the Prabhakar fractional derivatives. We provide various ways to determine the stability or asymptotic stability for these types of fractional differential systems. Some examples are applied to determine the stability of certain distributed-order systems.

On the stability and Lyapunov direct method for fractional difference model of BAM neural networks

2020 ◽  
Vol 38 (3) ◽  
pp. 2491-2501 ◽  
Author(s):  
Jehad Alzabut ◽  
Swati Tyagi ◽  
S.C. Martha
Keyword(s):  
Neural Networks ◽  
Direct Method ◽  
Bam Neural Networks ◽  
Lyapunov Direct Method ◽  
Difference Model ◽  
Fractional Difference ◽  
The Stability

scholarly journals Stability of Fractional Differential Equations with New Generalized Hattaf Fractional Derivative

2021 ◽  
Vol 2021 ◽  
pp. 1-7
Author(s):  
Khalid Hattaf
Keyword(s):  
Stability Analysis ◽  
Differential Equations ◽  
Fractional Derivative ◽  
Fractional Differential Equations ◽  
Fractional Derivatives ◽  
Direct Method ◽  
Lyapunov Direct Method ◽  
Science And Engineering ◽  
Fractional Differential ◽  
The Stability

This paper aims to study the stability of fractional differential equations involving the new generalized Hattaf fractional derivative which includes the most types of fractional derivatives with nonsingular kernels. The stability analysis is obtained by means of the Lyapunov direct method. First, some fundamental results and lemmas are established in order to achieve the goal of this study. Furthermore, the results related to exponential and Mittag–Leffler stability existing in recent studies are extended and generalized. Finally, illustrative examples are presented to show the applicability of our main results in some areas of science and engineering.

Asymptotic Stability Of Dynamic Equations With Two Fractional Terms: Continuous Versus Discrete Case

2015 ◽  
Vol 18 (2) ◽  
Author(s):  
Jan Čermák ◽  
Tomáš Kisela
Keyword(s):  
Asymptotic Stability ◽  
Fractional Derivatives ◽  
Fractional Difference ◽  
Caputo Fractional Derivatives ◽  
Stability Regions ◽  
The Stability ◽  
Fractional Terms ◽  
Discrete Stability ◽  
Stability Sets ◽  
Asymptotic Stability Conditions

AbstractThe paper discusses asymptotic stability conditions for the linear fractional difference equation∇with real coefficients a, b and real orders α > β > 0 such that α/β is a rational number. For given α, β, we describe various types of discrete stability regions in the (a, b)-plane and compare them with the stability regions recently derived for the underlying continuous patternDinvolving two Caputo fractional derivatives. Our analysis shows that discrete stability sets are larger and their structure much more rich than in the case of the continuous counterparts.

scholarly journals On uniform asymptotic stability for nonlinear integro-differential equations of Volterra type

2019 ◽  
pp. 161-166
Author(s):  
Natalia Sedova
Keyword(s):  
Stability Analysis ◽  
Asymptotic Stability ◽  
Sufficient Conditions ◽  
Zero Solution ◽  
Auxiliary Function ◽  
Uniform Asymptotic Stability ◽  
Volterra Type ◽  
Razumikhin Technique ◽  
The Stability ◽  
The Right

The specifics of the application of Razumikhin technique to the stability analysis of Volterra type integrodifferential equations are considered. The equation can be nonlinear and nonautonomous. We propose new sufficient conditions for uniform asymptotic stability of the zero solution using the phase space of a special construction and constraints on the right side of the equation. In the presented constraints we can analyze stability, relying not only on the behavior of the auxiliary function along the solutions, but also on the properties of the so called limiting equations.

scholarly journals Obtaining approximate region of asymptotic stability by computer algebra: A case study

2002 ◽  
Vol 20 (1) ◽  
pp. 56 ◽  
Author(s):  
S Prakash ◽  
J Vanualailai ◽  
T Soma
Keyword(s):  
Asymptotic Stability ◽  
Computer Algebra ◽  
System Analysis ◽  
Direct Method ◽  
Quantifier Elimination ◽  
Optimization Method ◽  
Analysis And Design ◽  
The Stability ◽  
Computer Algebra Software

One of the classical problems in nonlinear control system analysis and design is to find a region of asymptotic stability by the Direct Method of Lyapunov. This paper tentatively shows, via a numercial example, that this problem can be easily solved using Quantifier Elimination (QE). In particular, if the governing equations are described by differential equations containing only polynomials, then the problem can be conveniently solved by a computer algebra software packages such as Qepcad or Redlog. In our case study, we use a simple Lyapunov function and Qepcad to estimate the stability region, and the results are verified by an optimization method based on Lagrange's method.

scholarly journals On the Uniform Stability of Impulsive Lotka-Volterra Type Systems with Supremums

2018 ◽  
Vol 4 (2) ◽  
Author(s):  
Ivanka Stamova ◽  
Gani Stamov
Keyword(s):  
Asymptotic Stability ◽  
Lyapunov Method ◽  
Sufficient Conditions ◽  
Type Systems ◽  
Uniform Stability ◽  
Volterra Model ◽  
Uniform Asymptotic Stability ◽  
Volterra Type

In this paper we propose an impulsive n- species Lotka-Volterra model with supremums. By using Lyapunov method we give sufficient conditions for uniform stability and uniform asymptotic stability of the positive states.

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