Mathematical modeling of neuron model through fractal-fractional differentiation based on maxwell electromagnetic induction: application to neurodynamics.
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| Title: | Mathematical modeling of neuron model through fractal-fractional differentiation based on maxwell electromagnetic induction: application to neurodynamics. |
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| Authors: | Abro, Kashif Ali1,2 (AUTHOR) kashif.abro@faculty.muet.edu.pk, Atangana, Abdon1 (AUTHOR) |
| Source: | Neural Computing & Applications. Oct2024, Vol. 36 Issue 29, p18377-18385. 9p. |
| Subjects: | Electromagnetic induction, Neuron analysis, Integral operators, Fractal dimensions, Differential operators |
| Abstract: | The electrical activities of the reliable neuron models have different responses within intrinsic biophysical effects and can functionalize for asymmetric coexisting electrical activities under anti-monotonicity phenomenon. This manuscript presents mathematical analysis of neuron model based on Maxwell electromagnetic induction through newly proposed fractal-fractional differential and integral operators. The neuron model based on Maxwell electromagnetic induction changes with time along a fractal dimension that describes the cumulative chaotic phenomenon. The cumulative chaotic phenomenon of neuron model is mathematically modeled via exponential and Mittag–Leffler kernels with variable and fixed fractal and fractional orders. In order to exhibit fractal properties and memory effects, the neuron model is discretized by means of Adams–Bashforth-Moulton method that allows explicitly to compute the approximate solution of neuron model. The comparison of neuron model based on memory effect and fractal dimension have distinguished the evolution of neuron model at (i) variability of fractal order with fixed fractional order, (ii) variability of fractional order with fixed fractal order, and (iii) variability of fractal order as well fractional order. [ABSTRACT FROM AUTHOR] |
| Copyright of Neural Computing & Applications is the property of Springer Nature and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.) | |
| Database: | Engineering Source |
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| Header | DbId: egs DbLabel: Engineering Source An: 179738839 AccessLevel: 6 PubType: Academic Journal PubTypeId: academicJournal PreciseRelevancyScore: 0 |
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| Items | – Name: Title Label: Title Group: Ti Data: Mathematical modeling of neuron model through fractal-fractional differentiation based on maxwell electromagnetic induction: application to neurodynamics. – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22Abro%2C+Kashif+Ali%22">Abro, Kashif Ali</searchLink><relatesTo>1,2</relatesTo> (AUTHOR)<i> kashif.abro@faculty.muet.edu.pk</i><br /><searchLink fieldCode="AR" term="%22Atangana%2C+Abdon%22">Atangana, Abdon</searchLink><relatesTo>1</relatesTo> (AUTHOR) – Name: TitleSource Label: Source Group: Src Data: <searchLink fieldCode="JN" term="%22Neural+Computing+%26+Applications%22">Neural Computing & Applications</searchLink>. Oct2024, Vol. 36 Issue 29, p18377-18385. 9p. – Name: Subject Label: Subjects Group: Su Data: <searchLink fieldCode="DE" term="%22Electromagnetic+induction%22">Electromagnetic induction</searchLink><br /><searchLink fieldCode="DE" term="%22Neuron+analysis%22">Neuron analysis</searchLink><br /><searchLink fieldCode="DE" term="%22Integral+operators%22">Integral operators</searchLink><br /><searchLink fieldCode="DE" term="%22Fractal+dimensions%22">Fractal dimensions</searchLink><br /><searchLink fieldCode="DE" term="%22Differential+operators%22">Differential operators</searchLink> – Name: Abstract Label: Abstract Group: Ab Data: The electrical activities of the reliable neuron models have different responses within intrinsic biophysical effects and can functionalize for asymmetric coexisting electrical activities under anti-monotonicity phenomenon. This manuscript presents mathematical analysis of neuron model based on Maxwell electromagnetic induction through newly proposed fractal-fractional differential and integral operators. The neuron model based on Maxwell electromagnetic induction changes with time along a fractal dimension that describes the cumulative chaotic phenomenon. The cumulative chaotic phenomenon of neuron model is mathematically modeled via exponential and Mittag–Leffler kernels with variable and fixed fractal and fractional orders. In order to exhibit fractal properties and memory effects, the neuron model is discretized by means of Adams–Bashforth-Moulton method that allows explicitly to compute the approximate solution of neuron model. The comparison of neuron model based on memory effect and fractal dimension have distinguished the evolution of neuron model at (i) variability of fractal order with fixed fractional order, (ii) variability of fractional order with fixed fractal order, and (iii) variability of fractal order as well fractional order. [ABSTRACT FROM AUTHOR] – Name: AbstractSuppliedCopyright Label: Group: Ab Data: <i>Copyright of Neural Computing & Applications is the property of Springer Nature and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.) |
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| RecordInfo | BibRecord: BibEntity: Identifiers: – Type: doi Value: 10.1007/s00521-024-10047-y Languages: – Code: eng Text: English PhysicalDescription: Pagination: PageCount: 9 StartPage: 18377 Subjects: – SubjectFull: Electromagnetic induction Type: general – SubjectFull: Neuron analysis Type: general – SubjectFull: Integral operators Type: general – SubjectFull: Fractal dimensions Type: general – SubjectFull: Differential operators Type: general Titles: – TitleFull: Mathematical modeling of neuron model through fractal-fractional differentiation based on maxwell electromagnetic induction: application to neurodynamics. Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: Abro, Kashif Ali – PersonEntity: Name: NameFull: Atangana, Abdon IsPartOfRelationships: – BibEntity: Dates: – D: 11 M: 10 Text: Oct2024 Type: published Y: 2024 Identifiers: – Type: issn-print Value: 09410643 Numbering: – Type: volume Value: 36 – Type: issue Value: 29 Titles: – TitleFull: Neural Computing & Applications Type: main |
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