An application of artificial neural networks for solving fractional higher-order linear integro-differential equations
Abstract This ongoing work is vehemently dedicated to the investigation of a class of ordinary linear Volterra type integro-differential equations with fractional order in numerical mode. By replacing the unknown function by an appropriate multilayered feed-forward type neural structure, the fractio...
| Main Authors: | , , , , , , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
SpringerOpen
2023-07-01
|
| Series: | Boundary Value Problems |
| Subjects: | |
| Online Access: | https://doi.org/10.1186/s13661-023-01762-x |
| _version_ | 1797774045091987456 |
|---|---|
| author | T. Allahviranloo A. Jafarian R. Saneifard N. Ghalami S. Measoomy Nia F. Kiani U. Fernandez-Gamiz S. Noeiaghdam |
| author_facet | T. Allahviranloo A. Jafarian R. Saneifard N. Ghalami S. Measoomy Nia F. Kiani U. Fernandez-Gamiz S. Noeiaghdam |
| author_sort | T. Allahviranloo |
| collection | DOAJ |
| description | Abstract This ongoing work is vehemently dedicated to the investigation of a class of ordinary linear Volterra type integro-differential equations with fractional order in numerical mode. By replacing the unknown function by an appropriate multilayered feed-forward type neural structure, the fractional problem of such initial value is changed into a course of non-linear minimization equations, to some extent. Put differently, interest was sparked in structuring an optimized iterative first-order algorithm to estimate solutions for the origin fractional problem. On top of that, some computer simulation models exemplify the preciseness and well-functioning of the indicated iterative technique. The outstanding accomplished numerical outcomes conveniently reflect the productivity and competency of artificial neural network methods compared to customary approaches. |
| first_indexed | 2024-03-12T22:15:13Z |
| format | Article |
| id | doaj.art-b1c1120d16c642b88472b8cbe274575e |
| institution | Directory Open Access Journal |
| issn | 1687-2770 |
| language | English |
| last_indexed | 2024-03-12T22:15:13Z |
| publishDate | 2023-07-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Boundary Value Problems |
| spelling | doaj.art-b1c1120d16c642b88472b8cbe274575e2023-07-23T11:21:06ZengSpringerOpenBoundary Value Problems1687-27702023-07-012023111410.1186/s13661-023-01762-xAn application of artificial neural networks for solving fractional higher-order linear integro-differential equationsT. Allahviranloo0A. Jafarian1R. Saneifard2N. Ghalami3S. Measoomy Nia4F. Kiani5U. Fernandez-Gamiz6S. Noeiaghdam7Faculty of Engineering and Natural Sciences, Istinye UniversityDepartment of Mathematics, Urmia Branch, Islamic Azad UniversityDepartment of Mathematics, Urmia Branch, Islamic Azad UniversityDepartment of Mathematics, Urmia Branch, Islamic Azad UniversityDepartment of Mathematics, Urmia Branch, Islamic Azad UniversityComputer Engineering Department, Engineering Faculty, Fatih Sultan Mehmet Vakif UniversityNuclear Engineering and Fluid Mechanics Department, University of the Basque Country UPV/EHUIndustrial Mathematics Laboratory, Baikal School of BRICS, Irkutsk National Research Technical UniversityAbstract This ongoing work is vehemently dedicated to the investigation of a class of ordinary linear Volterra type integro-differential equations with fractional order in numerical mode. By replacing the unknown function by an appropriate multilayered feed-forward type neural structure, the fractional problem of such initial value is changed into a course of non-linear minimization equations, to some extent. Put differently, interest was sparked in structuring an optimized iterative first-order algorithm to estimate solutions for the origin fractional problem. On top of that, some computer simulation models exemplify the preciseness and well-functioning of the indicated iterative technique. The outstanding accomplished numerical outcomes conveniently reflect the productivity and competency of artificial neural network methods compared to customary approaches.https://doi.org/10.1186/s13661-023-01762-xHigher-order linear integro-differential equationArtificial neural network approachCaputo fractional derivativeLearning algorithmCost function |
| spellingShingle | T. Allahviranloo A. Jafarian R. Saneifard N. Ghalami S. Measoomy Nia F. Kiani U. Fernandez-Gamiz S. Noeiaghdam An application of artificial neural networks for solving fractional higher-order linear integro-differential equations Boundary Value Problems Higher-order linear integro-differential equation Artificial neural network approach Caputo fractional derivative Learning algorithm Cost function |
| title | An application of artificial neural networks for solving fractional higher-order linear integro-differential equations |
| title_full | An application of artificial neural networks for solving fractional higher-order linear integro-differential equations |
| title_fullStr | An application of artificial neural networks for solving fractional higher-order linear integro-differential equations |
| title_full_unstemmed | An application of artificial neural networks for solving fractional higher-order linear integro-differential equations |
| title_short | An application of artificial neural networks for solving fractional higher-order linear integro-differential equations |
| title_sort | application of artificial neural networks for solving fractional higher order linear integro differential equations |
| topic | Higher-order linear integro-differential equation Artificial neural network approach Caputo fractional derivative Learning algorithm Cost function |
| url | https://doi.org/10.1186/s13661-023-01762-x |
| work_keys_str_mv | AT tallahviranloo anapplicationofartificialneuralnetworksforsolvingfractionalhigherorderlinearintegrodifferentialequations AT ajafarian anapplicationofartificialneuralnetworksforsolvingfractionalhigherorderlinearintegrodifferentialequations AT rsaneifard anapplicationofartificialneuralnetworksforsolvingfractionalhigherorderlinearintegrodifferentialequations AT nghalami anapplicationofartificialneuralnetworksforsolvingfractionalhigherorderlinearintegrodifferentialequations AT smeasoomynia anapplicationofartificialneuralnetworksforsolvingfractionalhigherorderlinearintegrodifferentialequations AT fkiani anapplicationofartificialneuralnetworksforsolvingfractionalhigherorderlinearintegrodifferentialequations AT ufernandezgamiz anapplicationofartificialneuralnetworksforsolvingfractionalhigherorderlinearintegrodifferentialequations AT snoeiaghdam anapplicationofartificialneuralnetworksforsolvingfractionalhigherorderlinearintegrodifferentialequations AT tallahviranloo applicationofartificialneuralnetworksforsolvingfractionalhigherorderlinearintegrodifferentialequations AT ajafarian applicationofartificialneuralnetworksforsolvingfractionalhigherorderlinearintegrodifferentialequations AT rsaneifard applicationofartificialneuralnetworksforsolvingfractionalhigherorderlinearintegrodifferentialequations AT nghalami applicationofartificialneuralnetworksforsolvingfractionalhigherorderlinearintegrodifferentialequations AT smeasoomynia applicationofartificialneuralnetworksforsolvingfractionalhigherorderlinearintegrodifferentialequations AT fkiani applicationofartificialneuralnetworksforsolvingfractionalhigherorderlinearintegrodifferentialequations AT ufernandezgamiz applicationofartificialneuralnetworksforsolvingfractionalhigherorderlinearintegrodifferentialequations AT snoeiaghdam applicationofartificialneuralnetworksforsolvingfractionalhigherorderlinearintegrodifferentialequations |