Linear fractionally damped oscillator

DOI10.1155/2010/197020zbMath1207.34010arXiv0908.1683OpenAlexW1984598756WikidataQ58651233 ScholiaQ58651233MaRDI QIDQ606225

Mark Naber

Publication date: 16 November 2010

Published in: International Journal of Differential Equations (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0908.1683

Mathematics Subject Classification ID

Nonlinear oscillations and coupled oscillators for ordinary differential equations (34C15) Fractional ordinary differential equations (34A08)

Related Items (15)

Lyapunov stability of a fractionally damped oscillator with linear (anti-)damping ⋮ A free fractional viscous oscillator as a forced standard damped vibration ⋮ Modeling of a mass-spring-damper system by fractional derivatives with and without a singular kernel ⋮ A detailed analysis for the fundamental solution of fractional vibration equation ⋮ Fractional integro-differential calculus and its control-theoretical applications. II. fractional dynamic systems: modeling and hardware implementation ⋮ Unnamed Item ⋮ A pair of van der Pol oscillators coupled by fractional derivatives ⋮ Solution processes for second-order linear fractional differential equations with random inhomogeneous parts ⋮ Exact solutions of fractional order oscillation equation with two fractional derivative terms ⋮ The Cattaneo type space-time fractional heat conduction equation ⋮ Stability and delay sensitivity of neutral fractional-delay systems ⋮ Fractional calculus via Laplace transform and its application in relaxation processes ⋮ Solution of fractional order system of Bagley-Torvik equation using evolutionary computational intelligence ⋮ Long time behavior for a fractional Picard problem in a Hilbert space ⋮ Sufficient conditions for the exponential stability of nonlinear fractionally perturbed ODEs with multiple time delays

Cites Work

• Analytical solution of the Bagley-Torvik equation by Adomian decomposition method
• On the Appearance of the Fractional Derivative in the Behavior of Real Materials
• Chaotic and pseudochaotic attractors of perturbed fractional oscillator
• Fractional-order systems and PI/sup /spl lambda//D/sup /spl mu//-controllers

This page was built for publication: Linear fractionally damped oscillator