The Gα -scheme for Approximation of Fractional Derivatives: Application to the Dynamics of Dissipative Systems

DOI10.1177/1077546307087427zbMath1229.74054OpenAlexW1976454876WikidataQ118347377 ScholiaQ118347377MaRDI QIDQ3111033

A. C. Galucio, François Dubois, Jean-François Deü

Publication date: 17 January 2012

Published in: Journal of Vibration and Control (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1177/1077546307087427

zbMATH Keywords

fractional derivativesviscoelasticitylinear dynamicsmulti-step scheme

Mathematics Subject Classification ID

Vibrations in dynamical problems in solid mechanics (74H45) Fractional derivatives and integrals (26A33) Linear constitutive equations for materials with memory (74D05)

Related Items (6)

Decay of solutions to a water wave model with a nonlocal viscous term ⋮ Whitham equation with Landau damping on a half-line ⋮ Theoretical and numerical analysis of the decay rate of solutions to a water wave model with a nonlocal viscous dispersive term with Riemann-Liouville half derivative ⋮ A new unified approach to study fractional PDE equations on a half-line ⋮ A Neumann problem for the KdV equation with Landau damping on a half-line ⋮ Fractional derivative of Abel type on a half-line

Cites Work

• Treatment of dynamic systems with fractional derivatives without evaluating memory-integrals
• Computational algorithms for FE formulations involving fractional operators
• Finite element formulation of viscoelastic sandwich beams using fractional derivative operators
• An adaptation of the Gear scheme for fractional derivatives
• Algorithms for the fractional calculus: a selection of numerical methods
• Discretized Fractional Calculus
• Fractional calculus - A different approach to the analysis of viscoelastically damped structures

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