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Numerical approximations on the transient analysis of bioelectric phenomena at long time scales via the Mittag-Leffler function

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  • Hernández-Balaguera, Enrique

Abstract

This paper discusses the complexity of distributed relaxation processes in biological systems, particularly with regard to the slowest timescale phenomena that influence the modeling of physiological events. Specifically, our main interest is to determine the optimal excitation time at which the transient response, described in terms of relatively slow decays and memory effects, can be considered negligible. We estimate the time scale required for the Mittag-Leffler function to reach and stay within a range about the final value (dc “pseudo-steady state”). From numerical computations, we consider the problem of approximating holding times with common and rational (Padé-type) asymptotic approximations for comparative purposes. It is important to understand the physiological processes and to explore new mathematical models, based on efficient approximations, in order to design safe, controllable, and effective protocols for the electrical stimulation of excitable cells and the characterization of biological tissues.

Suggested Citation

  • Hernández-Balaguera, Enrique, 2021. "Numerical approximations on the transient analysis of bioelectric phenomena at long time scales via the Mittag-Leffler function," Chaos, Solitons & Fractals, Elsevier, vol. 145(C).
    • Handle: RePEc:eee:chsofr:v:145:y:2021:i:c:s096007792100120x
    DOI: 10.1016/j.chaos.2021.110768
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    1. Baleanu, Dumitru & Jajarmi, Amin & Mohammadi, Hakimeh & Rezapour, Shahram, 2020. "A new study on the mathematical modelling of human liver with Caputo–Fabrizio fractional derivative," Chaos, Solitons & Fractals, Elsevier, vol. 134(C).
    2. Tuan, Nguyen Huy & Mohammadi, Hakimeh & Rezapour, Shahram, 2020. "A mathematical model for COVID-19 transmission by using the Caputo fractional derivative," Chaos, Solitons & Fractals, Elsevier, vol. 140(C).
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