Academic Journal
Positive Solutions for a Class of Two-term Fractional q-derivative Boundary Value Problems with an Integral Condition.
| Τίτλος: | Positive Solutions for a Class of Two-term Fractional q-derivative Boundary Value Problems with an Integral Condition. |
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| Συγγραφείς: | Castro, L. P. |
| Πηγή: | Differential Equations & Dynamical Systems; Apr2026, Vol. 34 Issue 2, p499-524, 26p |
| Θεματικοί όροι: | Boundary value problems, Fractional calculus, Fractional integrals, Numerical solutions to boundary value problems, Nonlinear differential equations, Lipschitz continuity |
| Περίληψη: | We deduce different conditions to ensure positive solutions for a class of nonlinear two-term Riemann-Liouville fractional q-derivative boundary value problems which depends on a parameter and an integral condition. As a first step, we start by bringing this class of problems through a q-integral equation where its kernel is explicitly identified and its most characteristic properties are analysed. We then use an upper and lower solutions method, an appropriate cone and other techniques to obtain different types of conditions that ensure the existence of a positive solution to the class problems under study. Specific Lipschitz conditions are also identified to ensure the uniqueness of a continuous and positive solution. Finally, using a non-negative continuous concave functional on a cone and comparing the images it produces with the norm of potential solutions to the class of problems, other conditions are obtained that guarantee the existence of three (different) positive solutions to the class of problems under analysis. [ABSTRACT FROM AUTHOR] |
| Copyright of Differential Equations & Dynamical Systems is the property of Springer Nature 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.) | |
| Βάση Δεδομένων: | Complementary Index |
| FullText | Links: – Type: other Text: Availability: 0 CustomLinks: – Url: https://dx.doi.org/doi:10.1007/s12591-025-00751-z Name: EDS - Springer Nature Journals (s7799221) Category: fullText Text: View record at Springer |
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| Items | – Name: Title Label: Title Group: Ti Data: Positive Solutions for a Class of Two-term Fractional q-derivative Boundary Value Problems with an Integral Condition. – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22Castro%2C+L%2E+P%2E%22">Castro, L. P.</searchLink> – Name: TitleSource Label: Source Group: Src Data: Differential Equations & Dynamical Systems; Apr2026, Vol. 34 Issue 2, p499-524, 26p – Name: Subject Label: Subject Terms Group: Su Data: <searchLink fieldCode="DE" term="%22Boundary+value+problems%22">Boundary value problems</searchLink><br /><searchLink fieldCode="DE" term="%22Fractional+calculus%22">Fractional calculus</searchLink><br /><searchLink fieldCode="DE" term="%22Fractional+integrals%22">Fractional integrals</searchLink><br /><searchLink fieldCode="DE" term="%22Numerical+solutions+to+boundary+value+problems%22">Numerical solutions to boundary value problems</searchLink><br /><searchLink fieldCode="DE" term="%22Nonlinear+differential+equations%22">Nonlinear differential equations</searchLink><br /><searchLink fieldCode="DE" term="%22Lipschitz+continuity%22">Lipschitz continuity</searchLink> – Name: Abstract Label: Abstract Group: Ab Data: We deduce different conditions to ensure positive solutions for a class of nonlinear two-term Riemann-Liouville fractional q-derivative boundary value problems which depends on a parameter and an integral condition. As a first step, we start by bringing this class of problems through a q-integral equation where its kernel is explicitly identified and its most characteristic properties are analysed. We then use an upper and lower solutions method, an appropriate cone and other techniques to obtain different types of conditions that ensure the existence of a positive solution to the class problems under study. Specific Lipschitz conditions are also identified to ensure the uniqueness of a continuous and positive solution. Finally, using a non-negative continuous concave functional on a cone and comparing the images it produces with the norm of potential solutions to the class of problems, other conditions are obtained that guarantee the existence of three (different) positive solutions to the class of problems under analysis. [ABSTRACT FROM AUTHOR] – Name: Abstract Label: Group: Ab Data: <i>Copyright of Differential Equations & Dynamical Systems is the property of Springer Nature 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: 10.1007/s12591-025-00751-z Languages: – Code: eng Text: English PhysicalDescription: Pagination: PageCount: 26 StartPage: 499 Subjects: – SubjectFull: Boundary value problems Type: general – SubjectFull: Fractional calculus Type: general – SubjectFull: Fractional integrals Type: general – SubjectFull: Numerical solutions to boundary value problems Type: general – SubjectFull: Nonlinear differential equations Type: general – SubjectFull: Lipschitz continuity Type: general Titles: – TitleFull: Positive Solutions for a Class of Two-term Fractional q-derivative Boundary Value Problems with an Integral Condition. Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: Castro, L. P. IsPartOfRelationships: – BibEntity: Dates: – D: 01 M: 04 Text: Apr2026 Type: published Y: 2026 Identifiers: – Type: issn-print Value: 09713514 Numbering: – Type: volume Value: 34 – Type: issue Value: 2 Titles: – TitleFull: Differential Equations & Dynamical Systems Type: main |
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