Stability of Boundary Value Discrete Fractional Hybrid Equation of Second Type with Application to Heat Transfer with Fins
The development in the qualitative theory of fractional differential equations is accompanied by discrete analog which has been studied intensively in recent past. Suitable fixed point theorem is to be selected to study the boundary value discrete fractional equations due to the properties exhibited...
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| Format: | Article |
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MDPI AG
2022-09-01
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| Series: | Symmetry |
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| Online Access: | https://www.mdpi.com/2073-8994/14/9/1877 |
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| author | Wafa Shammakh A. George Maria Selvam Vignesh Dhakshinamoorthy Jehad Alzabut |
| author_facet | Wafa Shammakh A. George Maria Selvam Vignesh Dhakshinamoorthy Jehad Alzabut |
| author_sort | Wafa Shammakh |
| collection | DOAJ |
| description | The development in the qualitative theory of fractional differential equations is accompanied by discrete analog which has been studied intensively in recent past. Suitable fixed point theorem is to be selected to study the boundary value discrete fractional equations due to the properties exhibited by fractional difference operators. This article aims at investigating the stability results in the sense of Hyers and Ulam with application of Mittag–Leffler function hybrid fractional order difference equation of second type. The symmetric structure of the operators defined in this article is vital in establishing the existence results by using Krasnoselkii’s fixed point theorem. Banach contraction mapping principle and Krasnoselkii’s fixed point theorem are employed to establish the uniqueness and existence results for solution of fractional order discrete equation. A problem on heat transfer with fins is provided as an application to considered hybrid type fractional order difference equation and the stability results are demonstrated with simulations. |
| first_indexed | 2024-03-09T22:22:17Z |
| format | Article |
| id | doaj.art-835cea14814d4d48b182a8d139103189 |
| institution | Directory Open Access Journal |
| issn | 2073-8994 |
| language | English |
| last_indexed | 2024-03-09T22:22:17Z |
| publishDate | 2022-09-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Symmetry |
| spelling | doaj.art-835cea14814d4d48b182a8d1391031892023-11-23T19:12:25ZengMDPI AGSymmetry2073-89942022-09-01149187710.3390/sym14091877Stability of Boundary Value Discrete Fractional Hybrid Equation of Second Type with Application to Heat Transfer with FinsWafa Shammakh0A. George Maria Selvam1Vignesh Dhakshinamoorthy2Jehad Alzabut3Department of Mathematics, Faculty of Science, University of Jeddah, Jeddah 22233, Saudi ArabiaDepartment of Mathematics, Sacred Heart College (Autonomous), Tirupattur 635601, Tamil Nadu, IndiaDepartment of Mathematics, School of Advanced Sciences, Kalasalingam Academy of Research and Education, Krishnankoil, Srivilliputhur 626126, Tamil Nadu, IndiaDepartment of Mathematics and Sciences, Prince Sultan University, Riyadh 11586, Saudi ArabiaThe development in the qualitative theory of fractional differential equations is accompanied by discrete analog which has been studied intensively in recent past. Suitable fixed point theorem is to be selected to study the boundary value discrete fractional equations due to the properties exhibited by fractional difference operators. This article aims at investigating the stability results in the sense of Hyers and Ulam with application of Mittag–Leffler function hybrid fractional order difference equation of second type. The symmetric structure of the operators defined in this article is vital in establishing the existence results by using Krasnoselkii’s fixed point theorem. Banach contraction mapping principle and Krasnoselkii’s fixed point theorem are employed to establish the uniqueness and existence results for solution of fractional order discrete equation. A problem on heat transfer with fins is provided as an application to considered hybrid type fractional order difference equation and the stability results are demonstrated with simulations.https://www.mdpi.com/2073-8994/14/9/1877fractional orderdiscreteMittag–Leffler functionboundary value problemsHyers Ulam stability |
| spellingShingle | Wafa Shammakh A. George Maria Selvam Vignesh Dhakshinamoorthy Jehad Alzabut Stability of Boundary Value Discrete Fractional Hybrid Equation of Second Type with Application to Heat Transfer with Fins Symmetry fractional order discrete Mittag–Leffler function boundary value problems Hyers Ulam stability |
| title | Stability of Boundary Value Discrete Fractional Hybrid Equation of Second Type with Application to Heat Transfer with Fins |
| title_full | Stability of Boundary Value Discrete Fractional Hybrid Equation of Second Type with Application to Heat Transfer with Fins |
| title_fullStr | Stability of Boundary Value Discrete Fractional Hybrid Equation of Second Type with Application to Heat Transfer with Fins |
| title_full_unstemmed | Stability of Boundary Value Discrete Fractional Hybrid Equation of Second Type with Application to Heat Transfer with Fins |
| title_short | Stability of Boundary Value Discrete Fractional Hybrid Equation of Second Type with Application to Heat Transfer with Fins |
| title_sort | stability of boundary value discrete fractional hybrid equation of second type with application to heat transfer with fins |
| topic | fractional order discrete Mittag–Leffler function boundary value problems Hyers Ulam stability |
| url | https://www.mdpi.com/2073-8994/14/9/1877 |
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