Journal ArticleDOI
A new dissipation model based on memory mechanism
TLDR
The model of dissipation based on memory introduced by Caputo is generalized and checked with experimental dissipation curves of various materials.Abstract:
The model of dissipation based on memory introduced by Caputo is generalized and checked with experimental dissipation curves of various materialsread more
Citations
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Journal ArticleDOI
Fractional-order systems and PI/sup /spl lambda//D/sup /spl mu//-controllers
TL;DR: In this article, a fractional-order PI/sup/spl lambda/D/sup /spl mu/controller with fractionalorder integrator and fractional order differentiator is proposed.
Posted Content
Fractional Calculus: Some Basic Problems in Continuum and Statistical Mechanics
TL;DR: In this article, the authors review some applications of fractional calculus developed by the author (partly in collaboration with others) to treat some basic problems in continuum and statistical mechanics.
Journal ArticleDOI
Fractional calculus - A different approach to the analysis of viscoelastically damped structures
Ronald L. Bagley,Peter J. Torvik +1 more
TL;DR: In this paper, a fractional calculus is used to construct stress-strain relationships for viscoelastic materials and these relationships are used in the finite element analysis of damped structures and closed-form solutions to the equations of motion are found.
Journal ArticleDOI
Fractional Relaxation-Oscillation and Fractional Diffusion-Wave Phenomena
TL;DR: In this article, the authors introduced fractional derivatives of order α in time, with 0 for relaxation, diffusion, oscillations, and wave propagation, and showed that they are governed by simple differential equations of order 1 and 2 in time.
Book ChapterDOI
Multi-index Mittag-Leffler Functions
TL;DR: In this paper, Dzherbashian [Dzh60] defined a function with positive α 1 > 0, α 2 > 0 and real α 1, β 2, β 3, β 4, β 5, β 6, β 7, β 8, β 9, β 10, β 11, β 12, β 13, β 14, β 15, β 16, β 17, β 18, β 20, β 21, β 22, β 24
References
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Journal ArticleDOI
Linear Models of Dissipation whose Q is almost Frequency Independent-II
TL;DR: In this paper, a linear dissipative mechanism whose Q is almost frequency independent over large frequency ranges has been investigated by introducing fractional derivatives in the stressstrain relation, and a rigorous proof of the formulae to be used in obtaining the analytic expression of Q is given.
Book
Stress Waves in Solids
TL;DR: A large and growing number of original papers on both the experimental and the theoretical aspects of stress wave propagation is appearing in the scientific literature, and two international conferences solely concerned with the subject have been held during the last five years as mentioned in this paper.