Solvability of a Riemann–Liouville-Type Fractional-Impulsive Differential Equation with a Riemann–Stieltjes Integral Boundary Condition
In this work, we address the solvability of a Riemann–Liouville-type fractional-impulsive integral boundary value problem. Under some conditions on the spectral radius corresponding to the related linear operator, we use fixed-point methods to obtain several existence theorems for our problem. In pa...
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| Format: | Article |
| Language: | English |
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MDPI AG
2025-05-01
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| Series: | Fractal and Fractional |
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| Online Access: | https://www.mdpi.com/2504-3110/9/5/323 |
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| _version_ | 1850257520138911744 |
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| author | Keyu Zhang Donal O’Regan Jiafa Xu |
| author_facet | Keyu Zhang Donal O’Regan Jiafa Xu |
| author_sort | Keyu Zhang |
| collection | DOAJ |
| description | In this work, we address the solvability of a Riemann–Liouville-type fractional-impulsive integral boundary value problem. Under some conditions on the spectral radius corresponding to the related linear operator, we use fixed-point methods to obtain several existence theorems for our problem. In particular, we obtain the existence of multiple positive solutions via the Avery–Peterson fixed-point theorem. Note that our linear operator depends on the impulsive term and the integral boundary condition. |
| format | Article |
| id | doaj-art-c702e0f3263c4eec87d480e8566e6169 |
| institution | OA Journals |
| issn | 2504-3110 |
| language | English |
| publishDate | 2025-05-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Fractal and Fractional |
| spelling | doaj-art-c702e0f3263c4eec87d480e8566e61692025-08-20T01:56:24ZengMDPI AGFractal and Fractional2504-31102025-05-019532310.3390/fractalfract9050323Solvability of a Riemann–Liouville-Type Fractional-Impulsive Differential Equation with a Riemann–Stieltjes Integral Boundary ConditionKeyu Zhang0Donal O’Regan1Jiafa Xu2School of Mathematics, Qilu Normal University, Jinan 250013, ChinaSchool of Mathematical and Statistical Sciences, University of Galway, H91 TK33 Galway, IrelandSchool of Mathematical Sciences, Chongqing Normal University, Chongqing 401331, ChinaIn this work, we address the solvability of a Riemann–Liouville-type fractional-impulsive integral boundary value problem. Under some conditions on the spectral radius corresponding to the related linear operator, we use fixed-point methods to obtain several existence theorems for our problem. In particular, we obtain the existence of multiple positive solutions via the Avery–Peterson fixed-point theorem. Note that our linear operator depends on the impulsive term and the integral boundary condition.https://www.mdpi.com/2504-3110/9/5/323Riemann–Liouville-type fractional-order differential equationsintegral boundary value problemsimpulsepositive solutionsfixed-point methods |
| spellingShingle | Keyu Zhang Donal O’Regan Jiafa Xu Solvability of a Riemann–Liouville-Type Fractional-Impulsive Differential Equation with a Riemann–Stieltjes Integral Boundary Condition Fractal and Fractional Riemann–Liouville-type fractional-order differential equations integral boundary value problems impulse positive solutions fixed-point methods |
| title | Solvability of a Riemann–Liouville-Type Fractional-Impulsive Differential Equation with a Riemann–Stieltjes Integral Boundary Condition |
| title_full | Solvability of a Riemann–Liouville-Type Fractional-Impulsive Differential Equation with a Riemann–Stieltjes Integral Boundary Condition |
| title_fullStr | Solvability of a Riemann–Liouville-Type Fractional-Impulsive Differential Equation with a Riemann–Stieltjes Integral Boundary Condition |
| title_full_unstemmed | Solvability of a Riemann–Liouville-Type Fractional-Impulsive Differential Equation with a Riemann–Stieltjes Integral Boundary Condition |
| title_short | Solvability of a Riemann–Liouville-Type Fractional-Impulsive Differential Equation with a Riemann–Stieltjes Integral Boundary Condition |
| title_sort | solvability of a riemann liouville type fractional impulsive differential equation with a riemann stieltjes integral boundary condition |
| topic | Riemann–Liouville-type fractional-order differential equations integral boundary value problems impulse positive solutions fixed-point methods |
| url | https://www.mdpi.com/2504-3110/9/5/323 |
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