Existence and U-H Stability Results for Nonlinear Coupled Fractional Differential Equations with Boundary Conditions Involving Riemann–Liouville and Erdélyi–Kober Integrals
The purpose of this article is to discuss the existence, uniqueness, and Ulam–Hyers stability of solutions to a coupled system of fractional differential equations with Erdélyi–Kober and Riemann–Liouville integral boundary conditions. The Banach fixed point theorem is used to prove the uniqueness of...
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| Format: | Article |
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MDPI AG
2022-05-01
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| Series: | Fractal and Fractional |
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| Online Access: | https://www.mdpi.com/2504-3110/6/5/266 |
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| author | Muthaiah Subramanian P. Duraisamy C. Kamaleshwari Bundit Unyong R. Vadivel |
| author_facet | Muthaiah Subramanian P. Duraisamy C. Kamaleshwari Bundit Unyong R. Vadivel |
| author_sort | Muthaiah Subramanian |
| collection | DOAJ |
| description | The purpose of this article is to discuss the existence, uniqueness, and Ulam–Hyers stability of solutions to a coupled system of fractional differential equations with Erdélyi–Kober and Riemann–Liouville integral boundary conditions. The Banach fixed point theorem is used to prove the uniqueness of solutions, while the Leray–Schauder alternative is used to prove the existence of solutions. Furthermore, we conclude that the solution to the discussed problem is Hyers–Ulam stable. The results are illustrated with examples. |
| first_indexed | 2024-03-10T03:52:40Z |
| format | Article |
| id | doaj.art-dc8338b0493440ee89c3bef0e8a3f991 |
| institution | Directory Open Access Journal |
| issn | 2504-3110 |
| language | English |
| last_indexed | 2024-03-10T03:52:40Z |
| publishDate | 2022-05-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Fractal and Fractional |
| spelling | doaj.art-dc8338b0493440ee89c3bef0e8a3f9912023-11-23T11:03:45ZengMDPI AGFractal and Fractional2504-31102022-05-016526610.3390/fractalfract6050266Existence and U-H Stability Results for Nonlinear Coupled Fractional Differential Equations with Boundary Conditions Involving Riemann–Liouville and Erdélyi–Kober IntegralsMuthaiah Subramanian0P. Duraisamy1C. Kamaleshwari2Bundit Unyong3R. Vadivel4KPR Institute of Engineering and Technology, Coimbatore 641 407, IndiaDepartment of Mathematics, Gobi Arts and Science College, Gobichettipalayam 638 453, IndiaDepartment of Mathematics, Gobi Arts and Science College, Gobichettipalayam 638 453, IndiaDepartment of Mathematics, Faculty of Science and Technology, Phuket Rajabhat University, Phuket 83000, ThailandDepartment of Mathematics, Faculty of Science and Technology, Phuket Rajabhat University, Phuket 83000, ThailandThe purpose of this article is to discuss the existence, uniqueness, and Ulam–Hyers stability of solutions to a coupled system of fractional differential equations with Erdélyi–Kober and Riemann–Liouville integral boundary conditions. The Banach fixed point theorem is used to prove the uniqueness of solutions, while the Leray–Schauder alternative is used to prove the existence of solutions. Furthermore, we conclude that the solution to the discussed problem is Hyers–Ulam stable. The results are illustrated with examples.https://www.mdpi.com/2504-3110/6/5/266coupled systemErdélyi–Kober integralsRiemann–Liouville integralsexistenceUlam–Hyers stabilityfixed point |
| spellingShingle | Muthaiah Subramanian P. Duraisamy C. Kamaleshwari Bundit Unyong R. Vadivel Existence and U-H Stability Results for Nonlinear Coupled Fractional Differential Equations with Boundary Conditions Involving Riemann–Liouville and Erdélyi–Kober Integrals Fractal and Fractional coupled system Erdélyi–Kober integrals Riemann–Liouville integrals existence Ulam–Hyers stability fixed point |
| title | Existence and U-H Stability Results for Nonlinear Coupled Fractional Differential Equations with Boundary Conditions Involving Riemann–Liouville and Erdélyi–Kober Integrals |
| title_full | Existence and U-H Stability Results for Nonlinear Coupled Fractional Differential Equations with Boundary Conditions Involving Riemann–Liouville and Erdélyi–Kober Integrals |
| title_fullStr | Existence and U-H Stability Results for Nonlinear Coupled Fractional Differential Equations with Boundary Conditions Involving Riemann–Liouville and Erdélyi–Kober Integrals |
| title_full_unstemmed | Existence and U-H Stability Results for Nonlinear Coupled Fractional Differential Equations with Boundary Conditions Involving Riemann–Liouville and Erdélyi–Kober Integrals |
| title_short | Existence and U-H Stability Results for Nonlinear Coupled Fractional Differential Equations with Boundary Conditions Involving Riemann–Liouville and Erdélyi–Kober Integrals |
| title_sort | existence and u h stability results for nonlinear coupled fractional differential equations with boundary conditions involving riemann liouville and erdelyi kober integrals |
| topic | coupled system Erdélyi–Kober integrals Riemann–Liouville integrals existence Ulam–Hyers stability fixed point |
| url | https://www.mdpi.com/2504-3110/6/5/266 |
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