The Lambert function method in qualitative analysis of fractional delay differential equations

DOI10.1007/s13540-023-00176-xzbMath1522.34103OpenAlexW4380985603MaRDI QIDQ6073817

Tomáš Kisela, Jan Čermák, Luděk Nechvátal

Publication date: 12 October 2023

Published in: Fractional Calculus \& Applied Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s13540-023-00176-x

zbMATH Keywords

stabilityasymptotic behaviorLambert functionfractional delay differential equation

Mathematics Subject Classification ID

Asymptotic theory of functional-differential equations (34K25) Stability theory of functional-differential equations (34K20) Functional-differential equations with fractional derivatives (34K37)

Cites Work

• Unnamed Item
• Unnamed Item
• On parameter dependence of exponential stability of equilibrium solutions in differential equations with a single constant delay
• Finite time stability of fractional delay differential equations
• Analytical and numerical methods for the stability analysis of linear fractional delay differential equations
• Asymptotic properties of fractional delay differential equations
• Robust stability analysis of linear time-delay systems by Lambert \(W\) function: some extreme point results
• Finite time stability analysis of \(PD^\alpha\) fractional control of robotic time-delay systems
• Fractional differential equations with a constant delay: stability and asymptotics of solutions
• On the Lambert \(w\) function
• Analytical stability bound for a class of delayed fractional-order dynamic systems
• Solving fractional delay differential equations: a new approach
• Stabilization and destabilization of fractional oscillators via a delayed feedback control
• Exact solutions of fractional oscillation systems with pure delay
• Stability regions for fractional differential systems with a time delay
• On initial conditions for fractional delay differential equations
• Computing the Lambert \(W\) function in arbitrary-precision complex interval arithmetic
• A note on the use of the Lambert W function in the stability analysis of time-delay systems
• Stability and bifurcation analysis of a generalized scalar delay differential equation
• A Linearized Stability Theorem for Nonlinear Delay Fractional Differential Equations
• Numerical Methods for Delay Differential Equations
• On the existence and exponential stability for differential equations with multiple constant delays and nonlinearity depending on fractional substantial integrals