Existence and Ulam–Hyers Stability Analysis for Coupled Differential Equations of Fractional-Order with Nonlocal Generalized Conditions via Generalized Liouville–Caputo Derivative
In this paper, we investigate the existence and Hyers–Ulam stability of a coupled differential equations of fractional-order with multi-point (discrete) and integral boundary conditions that are related to Katugampola integrals. This manuscript can be categorized into four parts: The Leray–Schauder...
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| Format: | Article |
| Language: | English |
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MDPI AG
2022-10-01
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| Series: | Fractal and Fractional |
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| Online Access: | https://www.mdpi.com/2504-3110/6/11/629 |
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| author | Muthaiah Subramanian Shorog Aljoudi |
| author_facet | Muthaiah Subramanian Shorog Aljoudi |
| author_sort | Muthaiah Subramanian |
| collection | DOAJ |
| description | In this paper, we investigate the existence and Hyers–Ulam stability of a coupled differential equations of fractional-order with multi-point (discrete) and integral boundary conditions that are related to Katugampola integrals. This manuscript can be categorized into four parts: The Leray–Schauder alternative and Krasnoselskii’s fixed point theorems are used to prove the existence of a solution in the first and third section. The second section emphasizes the analysis of uniqueness, which is based on the Banach fixed point theorem’s concept of contraction mapping, and the fourth section establishes the Hyers–Ulam stability results. We demonstrate Hyers–Ulam stability using the traditional functional analysis technique. Finally, the consequences are validated using examples. |
| first_indexed | 2024-03-09T19:04:07Z |
| format | Article |
| id | doaj.art-0387074abe7e4b5f94c8265175edb133 |
| institution | Directory Open Access Journal |
| issn | 2504-3110 |
| language | English |
| last_indexed | 2024-03-09T19:04:07Z |
| publishDate | 2022-10-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Fractal and Fractional |
| spelling | doaj.art-0387074abe7e4b5f94c8265175edb1332023-11-24T04:45:06ZengMDPI AGFractal and Fractional2504-31102022-10-0161162910.3390/fractalfract6110629Existence and Ulam–Hyers Stability Analysis for Coupled Differential Equations of Fractional-Order with Nonlocal Generalized Conditions via Generalized Liouville–Caputo DerivativeMuthaiah Subramanian0Shorog Aljoudi1Department of Mathematics, KPR Institute of Engineering and Technology Coimbatore, Tamilnadu 641407, IndiaDepartment of Mathematics and Statistics, Collage of Science, Taif University, P.O. Box 11099, Taif 21944, Saudi ArabiaIn this paper, we investigate the existence and Hyers–Ulam stability of a coupled differential equations of fractional-order with multi-point (discrete) and integral boundary conditions that are related to Katugampola integrals. This manuscript can be categorized into four parts: The Leray–Schauder alternative and Krasnoselskii’s fixed point theorems are used to prove the existence of a solution in the first and third section. The second section emphasizes the analysis of uniqueness, which is based on the Banach fixed point theorem’s concept of contraction mapping, and the fourth section establishes the Hyers–Ulam stability results. We demonstrate Hyers–Ulam stability using the traditional functional analysis technique. Finally, the consequences are validated using examples.https://www.mdpi.com/2504-3110/6/11/629generalized Liouville–Caputo derivativesgeneralized fractional integralsmulti- pointscoupled systemexistencefixed point |
| spellingShingle | Muthaiah Subramanian Shorog Aljoudi Existence and Ulam–Hyers Stability Analysis for Coupled Differential Equations of Fractional-Order with Nonlocal Generalized Conditions via Generalized Liouville–Caputo Derivative Fractal and Fractional generalized Liouville–Caputo derivatives generalized fractional integrals multi- points coupled system existence fixed point |
| title | Existence and Ulam–Hyers Stability Analysis for Coupled Differential Equations of Fractional-Order with Nonlocal Generalized Conditions via Generalized Liouville–Caputo Derivative |
| title_full | Existence and Ulam–Hyers Stability Analysis for Coupled Differential Equations of Fractional-Order with Nonlocal Generalized Conditions via Generalized Liouville–Caputo Derivative |
| title_fullStr | Existence and Ulam–Hyers Stability Analysis for Coupled Differential Equations of Fractional-Order with Nonlocal Generalized Conditions via Generalized Liouville–Caputo Derivative |
| title_full_unstemmed | Existence and Ulam–Hyers Stability Analysis for Coupled Differential Equations of Fractional-Order with Nonlocal Generalized Conditions via Generalized Liouville–Caputo Derivative |
| title_short | Existence and Ulam–Hyers Stability Analysis for Coupled Differential Equations of Fractional-Order with Nonlocal Generalized Conditions via Generalized Liouville–Caputo Derivative |
| title_sort | existence and ulam hyers stability analysis for coupled differential equations of fractional order with nonlocal generalized conditions via generalized liouville caputo derivative |
| topic | generalized Liouville–Caputo derivatives generalized fractional integrals multi- points coupled system existence fixed point |
| url | https://www.mdpi.com/2504-3110/6/11/629 |
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