Fractional dynamical behavior of electrical activity in a model of pancreatic β-cells

Bodo, Bertrand; Mvogo, Alain; Morfu, Savério

doi:10.1016/j.chaos.2017.04.036

Cited by 16 publications

(4 citation statements)

References 42 publications

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“…In [14], the authors reported a fractional-order Izhikevich system to obtain insights on distinct neuronal spike responses, including bursting, fast-, regular-spiking, and chattering, as the no-integer order varies. The functioning at electrical level of a fractional-order system of an isolated β-cell is presented in [15,16]. In [17], was reported the comparison among diverse scenarios, such as integer, constant, no-constant and fractional-order derivatives, in order to explain the memory index.…”

Section: Introductionmentioning

confidence: 99%

The Effect of a Non-Local Fractional Operator in an Asymmetrical Glucose-Insulin Regulatory System: Analysis, Synchronization and Electronic Implementation

2020

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For studying biological conditions with higher precision, the memory characteristics defined by the fractional-order versions of living dynamical systems have been pointed out as a meaningful approach. Therefore, we analyze the dynamics of a glucose-insulin regulatory system by applying a non-local fractional operator in order to represent the memory of the underlying system, and whose state-variables define the population densities of insulin, glucose, and β-cells, respectively. We focus mainly on four parameters that are associated with different disorders (type 1 and type 2 diabetes mellitus, hypoglycemia, and hyperinsulinemia) to determine their observation ranges as a relation to the fractional-order. Like many preceding works in biosystems, the resulting analysis showed chaotic behaviors related to the fractional-order and system parameters. Subsequently, we propose an active control scheme for forcing the chaotic regime (an illness) to follow a periodic oscillatory state, i.e., a disorder-free equilibrium. Finally, we also present the electronic realization of the fractional glucose-insulin regulatory model to prove the conceptual findings.

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Section: Introductionmentioning

confidence: 99%

The Effect of a Non-Local Fractional Operator in an Asymmetrical Glucose-Insulin Regulatory System: Analysis, Synchronization and Electronic Implementation

2020

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“…Fractional partial differential equations (FPDEs) have gained extensive attention in the field of scientific research due to their applications in physical systems [16][17][18], chemical reactions [19], life sciences [20], computer sciences [21], digital cryptography systems [22], secure communications [23], and financial models [24]. Numerous studies have been conducted to construct several methods for solving FPDEs [25][26][27][28][29][30][31][32][33].…”

Section: Introductionmentioning

confidence: 99%

Numerical Simulation of the Fractional Dispersion Advection Equations Based on the Lattice Boltzmann Model

Wang

Zhang

Yan

2020

Mathematical Problems in Engineering

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The fractional dispersion advection equations (FDAEs) have recently attracted considerable attention due to their extensive application in the fields of science and engineering. For example, it has been shown that the anomalous solute transport behaviour that exists in hydrology can be well explained by introducing FDAEs. Therefore, the study of FDAEs has profound significance for understanding real transport phenomena in nature. Nevertheless, the existing algorithms for the FDAEs are generally intricate and costly. Therefore, exploiting an efficient solution technique has been a concern for scientists. In an effort to overcome this challenge, a promising lattice Boltzmann (LB) model for the FDAEs is presented in this paper. The Riemann–Liouville definition and the Grünwald–Letnikov definition are introduced for the time derivatives. In addition, Chapman–Enskog analysis is applied to recover the FDAEs. To test the validity of the model, three numerical examples are carried out. In addition, a comparative study of the proposed model and the classical implicit finite difference scheme is also conducted. The numerical results show that the model is suitable for simulating FDAEs.

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“…The FC has played a significant role in modeling different kinds of diseases [17][18][19][20][21]. There are several fractional operators, such as Caputo and Caputo-Fabrizio, which have been applied to study the behavior of biological systems.…”

Section: Introductionmentioning

confidence: 99%

New aspects of poor nutrition in the life cycle within the fractional calculus

et al. 2018

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The nutrition of pregnant women is crucial for giving birth to a healthy baby and even for the health status of a nursing mother. In this paper, the poor nutrition in the life cycle of humans is explored in the fractional sense. The proposed model is examined via the Caputo fractional operator and a new one with Mittag-Leffler (ML) nonsingular kernel. The stability analysis as well as the existence and uniqueness of the solution are investigated, and an efficient numerical scheme is also designed for the approximate solution. Comparative numerical analysis of these two operators reveals that the model based on the new fractional derivative with ML kernel has a different asymptotic behavior to the classic Caputo. Thus, the new aspects of fractional calculus provide more flexible models which help us to adjust the dynamical behaviors of the real-world phenomena better.

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Fractional dynamical behavior of electrical activity in a model of pancreatic β-cells

Cited by 16 publications

References 42 publications

The Effect of a Non-Local Fractional Operator in an Asymmetrical Glucose-Insulin Regulatory System: Analysis, Synchronization and Electronic Implementation

The Effect of a Non-Local Fractional Operator in an Asymmetrical Glucose-Insulin Regulatory System: Analysis, Synchronization and Electronic Implementation

Numerical Simulation of the Fractional Dispersion Advection Equations Based on the Lattice Boltzmann Model

New aspects of poor nutrition in the life cycle within the fractional calculus

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