ArticleScientific reports2013
Measuring memory with the order of fractional derivative.
Article in Scientific reports, 2013. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Cited by 30 papers.
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Who cites it
30 citing papers in PubMed.
- Modeling remote healthcare adoption with fractional-order reaction-diffusion: stability and policy insights.Theory in biosciences = Theorie in den Biowissenschaften · 2026Article
- Analytical solutions of the time-fractional symmetric regularized long wave equation using the [Formula: see text] model expansion method.Scientific reports · 2025Article
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- Bridging the gap between models based on ordinary, delayed, and fractional differentials equations through integral kernels.Proceedings of the National Academy of Sciences of the United States of America · 2024Article
- Computational and stability analysis of Ebola virus epidemic model with piecewise hybrid fractional operator.PloS one · 2024Article
- Diverse electrical responses in a network of fractional-order conductance-based excitable Morris-Lecar systems.Scientific reports · 2023Article
- Dynamics of chaotic system based on circuit design with Ulam stability through fractal-fractional derivative with power law kernel.Scientific reports · 2023Article
- Numerical analysis of fractional coronavirus model with Atangana-Baleanu derivative in Liouville-Caputo sense.Indian journal of physics and proceedings of the Indian Association for the Cultivation of Science (2004) · 2023Article
- Combining Fractional Derivatives and Machine Learning: A Review.Entropy (Basel, Switzerland) · 2022Review
- The impact of a power law-induced memory effect on the SARS-CoV-2 transmission.Chaos, solitons, and fractals · 2022Article
- Quantifying the impact of ecological memory on the dynamics of interacting communities.PLoS computational biology · 2022Article
- Use of mathematical modelling to assess respiratory syncytial virus epidemiology and interventions: a literature review.Journal of mathematical biology · 2022Review
- Fractional model of MHD blood flow in a cylindrical tube containing magnetic particles.Scientific reports · 2022Article
- Fractional-Order Traveling Wave Approximations for a Fractional-Order Neural Field Model.Frontiers in computational neuroscience · 2022Article
- Possibility of information encoding/decoding using the memory effect in fractional-order capacitive devices.Scientific reports · 2021Article
- A fractional order SITR mathematical model for forecasting of transmission of COVID-19 of India with lockdown effect.Results in physics · 2021Article
- Diffusion through skin in the light of a fractional derivative approach: progress and challenges.Journal of pharmacokinetics and pharmacodynamics · 2021Review
- A Reliable Solution of Nonlinear Time Dependent Fractional Model of Ebola Virus Disease with Arbitrary Order Derivative in Liouville-Caputo Sense.International journal of applied and computational mathematics · 2021Article
- Event-based fractional order control.Journal of advanced research · 2020Review
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3 authors.
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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.
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