Polynomial-Based Minimization Approach for Solving Fractional-Order Differential Equations of Bratu Type.
Saved in:
| Title: | Polynomial-Based Minimization Approach for Solving Fractional-Order Differential Equations of Bratu Type. |
|---|---|
| Authors: | Oderinu, Razaq Adekola1 raoderinu@lautech.edu.ng, Yahaya, Ahmed Adeyi2 aayahaya@lautech.edu.ng, Taiwo, Musilimu3 musilimu.taiwo@fuhsi.edu.ng, Oyewumi, Adepeju Abimbola1 aaoyewumi53@lautech.edu.ng, Salaudeen, Kafilat Adebimpe4 salaudeenka@eauedoyo.edu.ng |
| Source: | IAENG International Journal of Applied Mathematics. Jun2026, Vol. 56 Issue 6, p2196-2210. 15p. |
| Subjects: | Fractional differential equations, Polynomial approximation, Nonlinear boundary value problems, Collocation methods, Caputo fractional derivatives, Boundary value problems |
| Abstract: | This paper provides an effective polynomial-based minimization strategy using the collocation method to solve linear and non-linear fractional-order boundary value problems (BVPs). The Caputo fractional order derivative is employed, while the Lagrange interpolating polynomial and Newton divided difference polynomial are utilized as basis functions. The proposed method is capable of solving linear and nonlinear boundary value problems under various boundary conditions, including the Bratu-type equation with Robin and mixed boundary conditions. Numerical findings indicate the accuracy and efficiency of the suggested technique. In addition, the method revealed the non-local and hereditary properties peculiar to fractional-order differential equations, which many numerical methods cannot provide. The technique provided a valuable tool for solving complex fractional-order BVPs in different domains, including science, engineering, and technology. [ABSTRACT FROM AUTHOR] |
| Copyright of IAENG International Journal of Applied Mathematics is the property of International Association of Engineers (IAENG) 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 |
| FullText | Links: – Type: pdflink Text: Availability: 0 |
|---|---|
| Header | DbId: egs DbLabel: Engineering Source An: 194195910 AccessLevel: 6 PubType: Academic Journal PubTypeId: academicJournal PreciseRelevancyScore: 0 |
| IllustrationInfo | |
| Items | – Name: Title Label: Title Group: Ti Data: Polynomial-Based Minimization Approach for Solving Fractional-Order Differential Equations of Bratu Type. – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22Oderinu%2C+Razaq+Adekola%22">Oderinu, Razaq Adekola</searchLink><relatesTo>1</relatesTo><i> raoderinu@lautech.edu.ng</i><br /><searchLink fieldCode="AR" term="%22Yahaya%2C+Ahmed+Adeyi%22">Yahaya, Ahmed Adeyi</searchLink><relatesTo>2</relatesTo><i> aayahaya@lautech.edu.ng</i><br /><searchLink fieldCode="AR" term="%22Taiwo%2C+Musilimu%22">Taiwo, Musilimu</searchLink><relatesTo>3</relatesTo><i> musilimu.taiwo@fuhsi.edu.ng</i><br /><searchLink fieldCode="AR" term="%22Oyewumi%2C+Adepeju+Abimbola%22">Oyewumi, Adepeju Abimbola</searchLink><relatesTo>1</relatesTo><i> aaoyewumi53@lautech.edu.ng</i><br /><searchLink fieldCode="AR" term="%22Salaudeen%2C+Kafilat+Adebimpe%22">Salaudeen, Kafilat Adebimpe</searchLink><relatesTo>4</relatesTo><i> salaudeenka@eauedoyo.edu.ng</i> – Name: TitleSource Label: Source Group: Src Data: <searchLink fieldCode="JN" term="%22IAENG+International+Journal+of+Applied+Mathematics%22">IAENG International Journal of Applied Mathematics</searchLink>. Jun2026, Vol. 56 Issue 6, p2196-2210. 15p. – Name: Subject Label: Subjects Group: Su Data: <searchLink fieldCode="DE" term="%22Fractional+differential+equations%22">Fractional differential equations</searchLink><br /><searchLink fieldCode="DE" term="%22Polynomial+approximation%22">Polynomial approximation</searchLink><br /><searchLink fieldCode="DE" term="%22Nonlinear+boundary+value+problems%22">Nonlinear boundary value problems</searchLink><br /><searchLink fieldCode="DE" term="%22Collocation+methods%22">Collocation methods</searchLink><br /><searchLink fieldCode="DE" term="%22Caputo+fractional+derivatives%22">Caputo fractional derivatives</searchLink><br /><searchLink fieldCode="DE" term="%22Boundary+value+problems%22">Boundary value problems</searchLink> – Name: Abstract Label: Abstract Group: Ab Data: This paper provides an effective polynomial-based minimization strategy using the collocation method to solve linear and non-linear fractional-order boundary value problems (BVPs). The Caputo fractional order derivative is employed, while the Lagrange interpolating polynomial and Newton divided difference polynomial are utilized as basis functions. The proposed method is capable of solving linear and nonlinear boundary value problems under various boundary conditions, including the Bratu-type equation with Robin and mixed boundary conditions. Numerical findings indicate the accuracy and efficiency of the suggested technique. In addition, the method revealed the non-local and hereditary properties peculiar to fractional-order differential equations, which many numerical methods cannot provide. The technique provided a valuable tool for solving complex fractional-order BVPs in different domains, including science, engineering, and technology. [ABSTRACT FROM AUTHOR] – Name: AbstractSuppliedCopyright Label: Group: Ab Data: <i>Copyright of IAENG International Journal of Applied Mathematics is the property of International Association of Engineers (IAENG) 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=194195910 |
| RecordInfo | BibRecord: BibEntity: Languages: – Code: eng Text: English PhysicalDescription: Pagination: PageCount: 15 StartPage: 2196 Subjects: – SubjectFull: Fractional differential equations Type: general – SubjectFull: Polynomial approximation Type: general – SubjectFull: Nonlinear boundary value problems Type: general – SubjectFull: Collocation methods Type: general – SubjectFull: Caputo fractional derivatives Type: general – SubjectFull: Boundary value problems Type: general Titles: – TitleFull: Polynomial-Based Minimization Approach for Solving Fractional-Order Differential Equations of Bratu Type. Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: Oderinu, Razaq Adekola – PersonEntity: Name: NameFull: Yahaya, Ahmed Adeyi – PersonEntity: Name: NameFull: Taiwo, Musilimu – PersonEntity: Name: NameFull: Oyewumi, Adepeju Abimbola – PersonEntity: Name: NameFull: Salaudeen, Kafilat Adebimpe IsPartOfRelationships: – BibEntity: Dates: – D: 01 M: 06 Text: Jun2026 Type: published Y: 2026 Identifiers: – Type: issn-print Value: 19929978 Numbering: – Type: volume Value: 56 – Type: issue Value: 6 Titles: – TitleFull: IAENG International Journal of Applied Mathematics Type: main |
| ResultId | 1 |
