Measuring memory with the order of fractional derivative
Open Access
- 5 December 2013
- journal article
- research article
- Published by Springer Science and Business Media LLC in Scientific Reports
- Vol. 3 (1), 3431
- https://doi.org/10.1038/srep03431
Abstract
Fractional derivative has a history as long as that of classical calculus, but it is much less popular than it should be. What is the physical meaning of fractional derivative? This is still an open problem. In modeling various memory phenomena, we observe that a memory process usually consists of two stages. One is short with permanent retention, and the other is governed by a simple model of fractional derivative. With the numerical least square method, we show that the fractional model perfectly fits the test data of memory phenomena in different disciplines, not only in mechanics, but also in biology and psychology. Based on this model, we find that a physical meaning of the fractional order is an index of memory.Keywords
This publication has 17 references indexed in Scilit:
- Initialized fractional differential equations with Riemann-Liouville fractional-order derivativeThe European Physical Journal Special Topics, 2011
- Application of Fractional Calculus for Dynamic Problems of Solid Mechanics: Novel Trends and Recent ResultsApplied Mechanics Reviews, 2009
- Fractional differentiation by neocortical pyramidal neuronsNature Neuroscience, 2008
- Viscoelastic creep of nitrogen ceramicsJournal of Materials Science Letters, 1986
- Viscoelastic properties of erythrocyte membranes in high-frequency electric fieldsNature, 1984
- Fractional calculus - A different approach to the analysis of viscoelastically damped structuresAIAA Journal, 1983
- On the application of fractional calculus for the formulation of viscoelastic modelsApplied Mathematical Modelling, 1979
- Simple Viscoelastic Model for the Stress Relaxation of Rubber VulcanizatesNature, 1968
- A general stress-strain-time formulaJournal of the Franklin Institute, 1943
- A new general law of deformationJournal of the Franklin Institute, 1921