On the Generalized Liouville–Caputo Type Fractional Differential Equations Supplemented with Katugampola Integral Boundary Conditions
In this study, we examine the existence and Hyers–Ulam stability of a coupled system of generalized Liouville–Caputo fractional order differential equations with integral boundary conditions and a connection to Katugampola integrals. In the first and third theorems, the Leray–Schauder alternative an...
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| Format: | Article |
| Language: | English |
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MDPI AG
2022-10-01
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| Series: | Symmetry |
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| Online Access: | https://www.mdpi.com/2073-8994/14/11/2273 |
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| author | Muath Awadalla Muthaiah Subramanian Kinda Abuasbeh Murugesan Manigandan |
| author_facet | Muath Awadalla Muthaiah Subramanian Kinda Abuasbeh Murugesan Manigandan |
| author_sort | Muath Awadalla |
| collection | DOAJ |
| description | In this study, we examine the existence and Hyers–Ulam stability of a coupled system of generalized Liouville–Caputo fractional order differential equations with integral boundary conditions and a connection to Katugampola integrals. In the first and third theorems, the Leray–Schauder alternative and Krasnoselskii’s fixed point theorem are used to demonstrate the existence of a solution. The Banach fixed point theorem’s concept of contraction mapping is used in the second theorem to emphasise the analysis of uniqueness, and the results for Hyers–Ulam stability are established in the next theorem. We establish the stability of Ulam–Hyers using conventional functional analysis. Finally, examples are used to support the results. When a generalized Liouville–Caputo (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>ρ</mi></semantics></math></inline-formula>) parameter is modified, asymmetric results are obtained. This study presents novel results that significantly contribute to the literature on this topic. |
| first_indexed | 2024-03-09T18:35:58Z |
| format | Article |
| id | doaj.art-30c62a022ebe40a89bd78393d9c49a57 |
| institution | Directory Open Access Journal |
| issn | 2073-8994 |
| language | English |
| last_indexed | 2024-03-09T18:35:58Z |
| publishDate | 2022-10-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Symmetry |
| spelling | doaj.art-30c62a022ebe40a89bd78393d9c49a572023-11-24T07:07:38ZengMDPI AGSymmetry2073-89942022-10-011411227310.3390/sym14112273On the Generalized Liouville–Caputo Type Fractional Differential Equations Supplemented with Katugampola Integral Boundary ConditionsMuath Awadalla0Muthaiah Subramanian1Kinda Abuasbeh2Murugesan Manigandan3Department of Mathematics and Statistics, College of Science, King Faisal University, Hafuf, Al Ahsa 31982, Saudi ArabiaDepartment of Mathematics, KPR Institute of Engineering and Technology, Coimbatore 641407, Tamil Nadu, IndiaDepartment of Mathematics and Statistics, College of Science, King Faisal University, Hafuf, Al Ahsa 31982, Saudi ArabiaDepartment of Mathematics, Sri Ramakrishna Mission Vidyalaya College of Arts and Science, Coimbatore 641020, Tamil Nadu, IndiaIn this study, we examine the existence and Hyers–Ulam stability of a coupled system of generalized Liouville–Caputo fractional order differential equations with integral boundary conditions and a connection to Katugampola integrals. In the first and third theorems, the Leray–Schauder alternative and Krasnoselskii’s fixed point theorem are used to demonstrate the existence of a solution. The Banach fixed point theorem’s concept of contraction mapping is used in the second theorem to emphasise the analysis of uniqueness, and the results for Hyers–Ulam stability are established in the next theorem. We establish the stability of Ulam–Hyers using conventional functional analysis. Finally, examples are used to support the results. When a generalized Liouville–Caputo (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>ρ</mi></semantics></math></inline-formula>) parameter is modified, asymmetric results are obtained. This study presents novel results that significantly contribute to the literature on this topic.https://www.mdpi.com/2073-8994/14/11/2273generalized fractional derivativesgeneralized fractional integralscoupled systemexistencefixed point |
| spellingShingle | Muath Awadalla Muthaiah Subramanian Kinda Abuasbeh Murugesan Manigandan On the Generalized Liouville–Caputo Type Fractional Differential Equations Supplemented with Katugampola Integral Boundary Conditions Symmetry generalized fractional derivatives generalized fractional integrals coupled system existence fixed point |
| title | On the Generalized Liouville–Caputo Type Fractional Differential Equations Supplemented with Katugampola Integral Boundary Conditions |
| title_full | On the Generalized Liouville–Caputo Type Fractional Differential Equations Supplemented with Katugampola Integral Boundary Conditions |
| title_fullStr | On the Generalized Liouville–Caputo Type Fractional Differential Equations Supplemented with Katugampola Integral Boundary Conditions |
| title_full_unstemmed | On the Generalized Liouville–Caputo Type Fractional Differential Equations Supplemented with Katugampola Integral Boundary Conditions |
| title_short | On the Generalized Liouville–Caputo Type Fractional Differential Equations Supplemented with Katugampola Integral Boundary Conditions |
| title_sort | on the generalized liouville caputo type fractional differential equations supplemented with katugampola integral boundary conditions |
| topic | generalized fractional derivatives generalized fractional integrals coupled system existence fixed point |
| url | https://www.mdpi.com/2073-8994/14/11/2273 |
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