Solvability of two-dimensional nonlinear singular Volterra integral equations with fractional order in Banach space and approximation of the solution of it.
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| Title: | Solvability of two-dimensional nonlinear singular Volterra integral equations with fractional order in Banach space and approximation of the solution of it. |
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| Authors: | Khezri, Samaneh Darvishi1, Rabbani, Mohsen1 mo.rabbani@iau.ac.ir, Arab, Reza1, Dadashi, Vahid1 |
| Source: | Mathematical Modelling & Analysis. 2026, Vol. 31 Issue 3, p407-430. 24p. |
| Subjects: | Banach spaces, Singular integrals, Fractional integrals, Uniqueness (Mathematics), Perturbation theory, Fixed point theory |
| Abstract: | In this article, existence and uniqueness of the solution for two-dimensional non-linear singular Volterra integral equations with fractional orders in a Banach space is discussed by utilizing the concept of the measure of non-compactness and fixed-point theorem. In fact, this kind of equations is a generalization of twodimensional Riemann-Liouville fractional non-linear integral equations. To approximate the solution of the above problem, we use modified homotopy perturbation with the help of Adomian polynomials. To validity of the derived results, we introduce an example in the field of singular non-linear integral equations. Hence, a semianalytic solution for given example is obtained ensuring satisfactory accuracy. Also, to ensure the effectiveness of the proposed method the results are compared with some other works. [ABSTRACT FROM AUTHOR] |
| Copyright of Mathematical Modelling & Analysis is the property of Vilnius Gediminas Technical University 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: 194823831 AccessLevel: 6 PubType: Academic Journal PubTypeId: academicJournal PreciseRelevancyScore: 0 |
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| Items | – Name: Title Label: Title Group: Ti Data: Solvability of two-dimensional nonlinear singular Volterra integral equations with fractional order in Banach space and approximation of the solution of it. – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22Khezri%2C+Samaneh+Darvishi%22">Khezri, Samaneh Darvishi</searchLink><relatesTo>1</relatesTo><br /><searchLink fieldCode="AR" term="%22Rabbani%2C+Mohsen%22">Rabbani, Mohsen</searchLink><relatesTo>1</relatesTo><i> mo.rabbani@iau.ac.ir</i><br /><searchLink fieldCode="AR" term="%22Arab%2C+Reza%22">Arab, Reza</searchLink><relatesTo>1</relatesTo><br /><searchLink fieldCode="AR" term="%22Dadashi%2C+Vahid%22">Dadashi, Vahid</searchLink><relatesTo>1</relatesTo> – Name: TitleSource Label: Source Group: Src Data: <searchLink fieldCode="JN" term="%22Mathematical+Modelling+%26+Analysis%22">Mathematical Modelling & Analysis</searchLink>. 2026, Vol. 31 Issue 3, p407-430. 24p. – Name: Subject Label: Subjects Group: Su Data: <searchLink fieldCode="DE" term="%22Banach+spaces%22">Banach spaces</searchLink><br /><searchLink fieldCode="DE" term="%22Singular+integrals%22">Singular integrals</searchLink><br /><searchLink fieldCode="DE" term="%22Fractional+integrals%22">Fractional integrals</searchLink><br /><searchLink fieldCode="DE" term="%22Uniqueness+%28Mathematics%29%22">Uniqueness (Mathematics)</searchLink><br /><searchLink fieldCode="DE" term="%22Perturbation+theory%22">Perturbation theory</searchLink><br /><searchLink fieldCode="DE" term="%22Fixed+point+theory%22">Fixed point theory</searchLink> – Name: Abstract Label: Abstract Group: Ab Data: In this article, existence and uniqueness of the solution for two-dimensional non-linear singular Volterra integral equations with fractional orders in a Banach space is discussed by utilizing the concept of the measure of non-compactness and fixed-point theorem. In fact, this kind of equations is a generalization of twodimensional Riemann-Liouville fractional non-linear integral equations. To approximate the solution of the above problem, we use modified homotopy perturbation with the help of Adomian polynomials. To validity of the derived results, we introduce an example in the field of singular non-linear integral equations. Hence, a semianalytic solution for given example is obtained ensuring satisfactory accuracy. Also, to ensure the effectiveness of the proposed method the results are compared with some other works. [ABSTRACT FROM AUTHOR] – Name: AbstractSuppliedCopyright Label: Group: Ab Data: <i>Copyright of Mathematical Modelling & Analysis is the property of Vilnius Gediminas Technical University 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: 10.3846/mma.2026.24019 Languages: – Code: eng Text: English PhysicalDescription: Pagination: PageCount: 24 StartPage: 407 Subjects: – SubjectFull: Banach spaces Type: general – SubjectFull: Singular integrals Type: general – SubjectFull: Fractional integrals Type: general – SubjectFull: Uniqueness (Mathematics) Type: general – SubjectFull: Perturbation theory Type: general – SubjectFull: Fixed point theory Type: general Titles: – TitleFull: Solvability of two-dimensional nonlinear singular Volterra integral equations with fractional order in Banach space and approximation of the solution of it. Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: Khezri, Samaneh Darvishi – PersonEntity: Name: NameFull: Rabbani, Mohsen – PersonEntity: Name: NameFull: Arab, Reza – PersonEntity: Name: NameFull: Dadashi, Vahid IsPartOfRelationships: – BibEntity: Dates: – D: 01 M: 07 Text: 2026 Type: published Y: 2026 Identifiers: – Type: issn-print Value: 13926292 Numbering: – Type: volume Value: 31 – Type: issue Value: 3 Titles: – TitleFull: Mathematical Modelling & Analysis Type: main |
| ResultId | 1 |
