Asymptotic Stability Of Dynamic Equations With Two Fractional Terms: Continuous Versus Discrete Case
-
Jan Čermák
and
Tomáš Kisela
Abstract
The paper discusses asymptotic stability conditions for the linear fractional difference equation
∇αy(n) + a∇βy(n) + by(n) = 0
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 pattern
Dαx(t) + aDβx(t) + bx(t) = 0
involving 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.
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Articles in the same Issue
- Contents
- Fcaa Related News, Events and Books (Fcaa–Volume 18–2–2015)
- New Results from Old Investigation: A Note on Fractional M-Dimensional Differential Operators. The Fractional Laplacian
- Pollutant Reduction of a Turbocharged Diesel Engine Using a Decentralized Mimo Crone Controller
- Experimental Implications of Bochner-Levy-Riesz Diffusion
- Fractional Diffusion on Bounded Domains
- On a System of Fractional Differential Equations with Coupled Integral Boundary Conditions
- A Numerical Approach for Fractional Order Riccati Differential Equation Using B-Spline Operational Matrix
- Solving Fractional Delay Differential Equations: A New Approach
- Formal Consistency Versus Actual Convergence Rates of Difference Schemes for Fractional-Derivative Boundary Value Problems
- Asymptotic Stability Of Dynamic Equations With Two Fractional Terms: Continuous Versus Discrete Case
- Analysis of Natural and Artificial Phenomena Using Signal Processing and Fractional Calculus
- Fractional Approach for Estimating Sap Velocity in Trees
- Fractional Calculus: Quo Vadimus? (Where are we Going?)
Articles in the same Issue
- Contents
- Fcaa Related News, Events and Books (Fcaa–Volume 18–2–2015)
- New Results from Old Investigation: A Note on Fractional M-Dimensional Differential Operators. The Fractional Laplacian
- Pollutant Reduction of a Turbocharged Diesel Engine Using a Decentralized Mimo Crone Controller
- Experimental Implications of Bochner-Levy-Riesz Diffusion
- Fractional Diffusion on Bounded Domains
- On a System of Fractional Differential Equations with Coupled Integral Boundary Conditions
- A Numerical Approach for Fractional Order Riccati Differential Equation Using B-Spline Operational Matrix
- Solving Fractional Delay Differential Equations: A New Approach
- Formal Consistency Versus Actual Convergence Rates of Difference Schemes for Fractional-Derivative Boundary Value Problems
- Asymptotic Stability Of Dynamic Equations With Two Fractional Terms: Continuous Versus Discrete Case
- Analysis of Natural and Artificial Phenomena Using Signal Processing and Fractional Calculus
- Fractional Approach for Estimating Sap Velocity in Trees
- Fractional Calculus: Quo Vadimus? (Where are we Going?)
