KFU. Card publication. Neural network method for solving fractional differential equations \alpha with the dirichlet problem

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FEDERAL UNIVERSITY

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NEURAL NETWORK METHOD FOR SOLVING FRACTIONAL DIFFERENTIAL EQUATIONS \ALPHA WITH THE DIRICHLET PROBLEM

Form of presentation

Articles in international journals and collections

Year of publication

2023

Authors, employees of KFU

Galimyanov Anis Fuatovich, author

Bibliographic description in the original language

Duc, N. T. Neural network method for solving fractional differential equations with the dirichlet problem / N. T. Duc, A. F. Galimyanov, I. Z. Akhmetov // 2023 International Russian Smart Industry Conference (SmartIndustryCon) / IEEE. - 2023. - Pp. 295-300, doi: 10.1109/SmartIndustryCon57312.2023.10110785.

Annotation

2023 International Russian Smart Industry Conference (SmartIndustryCon)

Keywords

fractional differential equations,Dirichlet?s problem, conformable fractional derivative, artificial neural network

The name of the journal

2023 International Russian Smart Industry Conference (SmartIndustryCon)

Publishing house

IEEE

URL

https://ieeexplore.ieee.org/abstract/document/10110785/keywords#keywords

Please use this ID to quote from or refer to the card

https://repository.kpfu.ru/eng/?p_id=280824&p_lang=2

Full metadata record

Field DC	Value	Language
dc.contributor.author	Galimyanov Anis Fuatovich	ru_RU
dc.date.accessioned	2023-01-01T00:00:00Z	ru_RU
dc.date.available	2023-01-01T00:00:00Z	ru_RU
dc.date.issued	2023	ru_RU
dc.identifier.citation	Duc, N. T. Neural network method for solving fractional differential equations with the dirichlet problem / N. T. Duc, A. F. Galimyanov, I. Z. Akhmetov // 2023 International Russian Smart Industry Conference (SmartIndustryCon) / IEEE. - 2023. - Pp. 295-300, doi: 10.1109/SmartIndustryCon57312.2023.10110785.	ru_RU
dc.identifier.uri	https://repository.kpfu.ru/eng/?p_id=280824&p_lang=2	ru_RU
dc.description.abstract	2023 International Russian Smart Industry Conference (SmartIndustryCon)	ru_RU
dc.description.abstract	In this paper, we have developed an artificial neural network (ANN) method for finding solutions to the Dirichlet problem for fractional order differential equations (FODEs) 0 <α<1 using the definition of a conformable fractional derivative. Here, we used a feedforward neural architecture, L-BFGS (Broyden ? Fletcher ? Goldfarb - Shanno) optimization method to minimize the error function and change the parameters (weights and biases). The main idea is that if the sum of the norms of the residuals of the equation on the domain of definition and the boundary conditions tends to zero when the unknown function y(x) is replaced by its neural network approximation N(x), then N(x) is an approximate solution of the differential equation. Some illustrative examples are given demonstrating the accuracy and efficiency of this method and comparing the results of the current method with mathematical results.	ru_RU
dc.language.iso	ru	ru_RU
dc.publisher	IEEE	ru_RU
dc.subject	fractional differential equations	ru_RU
dc.subject	Dirichlet?s problem	ru_RU
dc.subject	conformable fractional derivative	ru_RU
dc.subject	artificial neural network	ru_RU
dc.title	Neural network method for solving fractional differential equations \alpha with the dirichlet problem	ru_RU
dc.type	Articles in international journals and collections	ru_RU