Measuring memory with the order of fractional derivative

By M. Du, Zaihua Wang, Haiyan Hu. Scientific Reports, 2013

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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.

Subfields: Control and Systems Engineering, Modeling and Simulation

View Paper: https://www.semanticscholar.org/paper/472e8a323b670a0e4fa231bc1309de189e5e216d

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In Control and Systems Engineering

In Modeling and Simulation

Citations in the corpus

Fractional-order PD control at Hopf bifurcations in a fractional-order congestion control system (2017, background): “Past several years have witnessed the wide applications of fractional calculus, involving biology [1–3], physics [4,5], psychology [6], engineering [7,8], etc.”
A fractional calculus approach to the dynamic optimization of biological reactive systems. Part I: Fractional models for biological reactions (2014, methodology): “Diethelm (2013) used a similar but slightly different technique to formulate a fractional model from an ordinary model representing the dynamics of an outbreak of dengue fever; a population balance has to be satisfied on that problem. Starting from an ordinary model, Diethelm (2013) replaced the ord”
The Role of Fractional Time-Derivative Operators on Anomalous Diffusion (2017, background): “0 ρ(x, t′) (t − t′)1−α dt′ , (2) where 0 < α < 1 is the fractional order exponent (or the anomalous exponent), a quantity that can be interpreted as an index of memory in empirical systems [24].”