Mathematical modelling of fractional order circuit elements and bioimpedance applications

Moreles, Miguel Ángel; Lainez, Rafael

doi:10.1016/j.cnsns.2016.10.020

Cited by 66 publications

(36 citation statements)

References 9 publications

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“…Descriptions employing differential calculus of fractional order have been extended to include phenomena occurring in real inductances. This comprises real coils (loss coils) with the skin effect, especially those with soft ferromagnetic cores, or containing electronic active systems, e.g., a generalized impedance converter (GIC) [15] and a coil with a fractional mutual inductance [16]. Other applications of fractional-order elements for materials and solutions described by chemical reactions are presented in [17,18].…”

Section: Introductionmentioning

confidence: 99%

Properties of Fractional-Order Magnetic Coupling

et al. 2020

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This paper presents the properties of fractional-order magnetic coupling. The difficulties connected with the analysis of two coils in dynamic states, resulting from the classical approach, provided motivation for studying the properties of fractional-order magnetic coupling. These difficulties arise from failure to comply with the commutation laws, i.e., a sudden power disappearance in the primary winding caused by a switch-mode power supply. Theoretically, under ideal conditions, a sudden power disappearance in the coil is, according to the classical method, manifested by a sudden voltage surge in the form of the Dirac delta function. As is well-known, it is difficult to obtain such ideal conditions in practice; the time of current disappearance does not equal zero due to the circuit breaker’s imperfection (even when electronic circuit breakers are used, the time equals several hundred nanoseconds). Furthermore, it is necessary to take into account phenomena occurring in real inductances, such as the skin effect, the influence of the ferromagnetic core and many other factors. It would be very difficult to model all these phenomena using classical differential calculus. The application of fractional-order differential calculus makes it possible to model them in a simple way by appropriate selection of coefficients and fractional-order derivatives. It should be mentioned that the analysis could be used, for example, in the case of high-voltage generation systems, including spark ignition systems of internal combustion engines. The use of fractional-order differential calculus will allow for more accurate modeling of phenomena occurring in such systems.

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Section: Introductionmentioning

confidence: 99%

Properties of Fractional-Order Magnetic Coupling

et al. 2020

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“…Special "fractional" R, L, C elements have been introduced in the paper [10]. Consequently, special coefficient, ensuring dimensional uniformity has been incorporated in the equations that describe "fractional circuit".…”

Section: Fractional Derivatives In Electrical Circuit Theorymentioning

confidence: 99%

“…In the paper [10] the Maxwell equations have been presented in the form of (13) and (14), amended with the continuity laws instead of Eqs. (15) and (16).…”

Section: Fractional Derivatives In Electrical Circuit Theorymentioning

confidence: 99%

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Fractional derivatives in electrical circuit theory – critical remarks

Sikora¹

2017

Archives of Electrical Engineering

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“…Recently it is showed that the fractional model perfectly fits the test data of memory phenomena in different disciplines [46] they have found that a possible physical meaning of the fractional order is an index of memory. From this viewpoint fractional calculus has found many applications in new research on physics of biological structures and living organisms, from DNA dynamics [47][48][49] to protein folding [50], cancer cells [51], tumor-immune system [52], modeling of some human autoimmune diseases such as psoriasis [53], bioimpedance [54], spiking neurons [55], and also the transport of drugs across biological materials and human skin [56] and electrical impedance applied to human skin [57] and even modeling of HIV dynamics [58].…”

Section: Fractional Calculus In Bioscience and Biomedicinementioning

confidence: 99%

Fractional Dynamics in Bioscience and Biomedicine and the Physics of Cancer

Nasrolahpour

2017

Preprint

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Almost all phenomena and structures in nature exhibit some degrees of fractionality or fractality. Fractional calculus and fractal theory are two interrelated concepts. In this article we study the memory effects in nature and particularly in biological structures. Based on this fact that natural way to incorporate memory effects in the modeling of various phenomena and dealing with complexities is using of fractional calculus, in this article we present different examples in various branch of science from cosmology to biology and we investigate this idea that are we able to describe all of such these phenomena using the well-know and powerful tool of fractional calculus. In particular we focus on fractional calculus approach as an effective tool for better understanding of physics of living systems and organism and especially physics of cancer.Keywords: Fractional Dynamics; Memory Effect; Biological Structures; Physics of Cancer IntroductionThe concept of memory effect plays an important role in a large number of phenomena in different contexts and systems from biological structures to cosmological phenomena. For instance: memory effects in nanoscale systems [1,2], optical memory effect [3], gravitational and cosmological memory effect (which means: the induction of a permanent change in the relative separation of the test particles when gravitational radiation passes through a configuration of test particles that make up a gravitational wave detector) [4], memory effects in gene regulatory networks [5], memory effects in economics [6] have been investigated. In addition other kinds of memory effect including: shape memory effect [7][8][9][10], magnetic shape memory effect [11] and temperature memory effect [12] have been also considered in recent years. In all above mentioned references authors have used the standard calculus, however nowadays it is well-known that a natural way to incorporate memory effects in the modeling of various phenomena is using of fractional calculus. On the other hand almost all phenomena and structures in nature exhibit some degrees and levels of fractionality or fractality (low or high level or something between them), also nowadays it is well-known that there is a close relation between fractality and fractionality. In this work we investigate this idea that are we able to describe all of such these phenomena using the well-know and powerful tool of fractional calculus. Therefore for this purpose in the following, concepts of fractality and fractional dynamics are briefly reviewed respectively in Sec. 2.Then in Sec. 3 we introduce fractional calculus as a powerful tool for modeling of memory effects in different context and we present some important applications. At last, in Sec. 4, we will present some conclusions.

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Mathematical modelling of fractional order circuit elements and bioimpedance applications

Cited by 66 publications

References 9 publications

Properties of Fractional-Order Magnetic Coupling

Properties of Fractional-Order Magnetic Coupling

Fractional derivatives in electrical circuit theory – critical remarks

Fractional Dynamics in Bioscience and Biomedicine and the Physics of Cancer

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