A Hyperaccurate Semi–Analytical Method With Error Bound Analysis for Treating Fractional Integral Equations With Functional Kernels and Variable Delays.
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| Title: | A Hyperaccurate Semi–Analytical Method With Error Bound Analysis for Treating Fractional Integral Equations With Functional Kernels and Variable Delays. |
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| Authors: | Kürkçü, Ömür Kıvanç1 (AUTHOR) omurkivanc@outlook.com |
| Source: | International Journal of Numerical Modelling. May/Jun2025, Vol. 38 Issue 3, p1-11. 11p. |
| Subjects: | Functional equations, Integral calculus, Mean value theorems, Fractional integrals, Integral equations |
| Abstract: | This study is concerned with treating the fractional integral equations with functional kernels and variable delays, introducing a hyperaccurate semi–analytical method based on the Stieltjes–Wigert polynomials, matrix expansions, and the Laplace transform. After analytically converting the terms in the governing equation into the matrix expansions of the Stieltjes–Wigert polynomials type at the collocation points, the method gathers these matrices into a unique matrix equation and then readily solves it by an elimination technique. The residual improvement technique is also introduced to correct the obtained solutions. The residual error bound analysis is theoretically proved via algebraical properties and the mean value theorem for fractional integral calculus, respectively. Six model equations are treated via the method, which runs on a devised computer program. Based on the outcomes, the method is straightforward to treat model equations and to encode its mainframe on a mathematical software. [ABSTRACT FROM AUTHOR] |
| Copyright of International Journal of Numerical Modelling is the property of Wiley-Blackwell 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: 186112804 AccessLevel: 6 PubType: Academic Journal PubTypeId: academicJournal PreciseRelevancyScore: 0 |
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| Items | – Name: Title Label: Title Group: Ti Data: A Hyperaccurate Semi–Analytical Method With Error Bound Analysis for Treating Fractional Integral Equations With Functional Kernels and Variable Delays. – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22Kürkçü%2C+Ömür+Kıvanç%22">Kürkçü, Ömür Kıvanç</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> omurkivanc@outlook.com</i> – Name: TitleSource Label: Source Group: Src Data: <searchLink fieldCode="JN" term="%22International+Journal+of+Numerical+Modelling%22">International Journal of Numerical Modelling</searchLink>. May/Jun2025, Vol. 38 Issue 3, p1-11. 11p. – Name: Subject Label: Subjects Group: Su Data: <searchLink fieldCode="DE" term="%22Functional+equations%22">Functional equations</searchLink><br /><searchLink fieldCode="DE" term="%22Integral+calculus%22">Integral calculus</searchLink><br /><searchLink fieldCode="DE" term="%22Mean+value+theorems%22">Mean value theorems</searchLink><br /><searchLink fieldCode="DE" term="%22Fractional+integrals%22">Fractional integrals</searchLink><br /><searchLink fieldCode="DE" term="%22Integral+equations%22">Integral equations</searchLink> – Name: Abstract Label: Abstract Group: Ab Data: This study is concerned with treating the fractional integral equations with functional kernels and variable delays, introducing a hyperaccurate semi–analytical method based on the Stieltjes–Wigert polynomials, matrix expansions, and the Laplace transform. After analytically converting the terms in the governing equation into the matrix expansions of the Stieltjes–Wigert polynomials type at the collocation points, the method gathers these matrices into a unique matrix equation and then readily solves it by an elimination technique. The residual improvement technique is also introduced to correct the obtained solutions. The residual error bound analysis is theoretically proved via algebraical properties and the mean value theorem for fractional integral calculus, respectively. Six model equations are treated via the method, which runs on a devised computer program. Based on the outcomes, the method is straightforward to treat model equations and to encode its mainframe on a mathematical software. [ABSTRACT FROM AUTHOR] – Name: AbstractSuppliedCopyright Label: Group: Ab Data: <i>Copyright of International Journal of Numerical Modelling is the property of Wiley-Blackwell 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.) |
| PLink | https://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=egs&AN=186112804 |
| RecordInfo | BibRecord: BibEntity: Identifiers: – Type: doi Value: 10.1002/jnm.70061 Languages: – Code: eng Text: English PhysicalDescription: Pagination: PageCount: 11 StartPage: 1 Subjects: – SubjectFull: Functional equations Type: general – SubjectFull: Integral calculus Type: general – SubjectFull: Mean value theorems Type: general – SubjectFull: Fractional integrals Type: general – SubjectFull: Integral equations Type: general Titles: – TitleFull: A Hyperaccurate Semi–Analytical Method With Error Bound Analysis for Treating Fractional Integral Equations With Functional Kernels and Variable Delays. Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: Kürkçü, Ömür Kıvanç IsPartOfRelationships: – BibEntity: Dates: – D: 01 M: 05 Text: May/Jun2025 Type: published Y: 2025 Identifiers: – Type: issn-print Value: 08943370 Numbering: – Type: volume Value: 38 – Type: issue Value: 3 Titles: – TitleFull: International Journal of Numerical Modelling Type: main |
| ResultId | 1 |
