Ulam Stability of Fractional Hybrid Sequential Integro-Differential Equations with Existence and Uniqueness Theory
In this paper, a variety of boundary value problems (BVPs) known as hybrid fractional sequential integro-differential equations (HFSIDs) with two point orders (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow&...
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| Format: | Article |
| Language: | English |
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MDPI AG
2022-11-01
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| Series: | Symmetry |
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| Online Access: | https://www.mdpi.com/2073-8994/14/11/2438 |
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| author | Obaid Algahtani |
| author_facet | Obaid Algahtani |
| author_sort | Obaid Algahtani |
| collection | DOAJ |
| description | In this paper, a variety of boundary value problems (BVPs) known as hybrid fractional sequential integro-differential equations (HFSIDs) with two point orders (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi mathvariant="fraktur">p</mi><mo>,</mo><mi mathvariant="fraktur">q</mi></mrow></semantics></math></inline-formula>) are investigated. The uniqueness and existence of the solution are discussed via Banach fixed-point theorems. Certain particular theorems associated with Hyers–Ulam and Hyers–Ulam–Rassias stability to the solution, as well as the uniqueness and existence of the solution of the BVPs are studied. The results are illustrated with some particular examples, and the numerical data are analyzed for confirmation of the results. The results obtained in this work are simple and can easily be applicable to physical systems. Furthermore, symmetry analysis of fractional differential equations and HFSIDs are also presented. This is due to the fact that the aforementioned analysis plays a significant role in both the optimization and qualitative theory of fractional differential equations. |
| first_indexed | 2024-03-09T17:57:34Z |
| format | Article |
| id | doaj.art-d6b98f4fe9ab47a296e180db1b139be9 |
| institution | Directory Open Access Journal |
| issn | 2073-8994 |
| language | English |
| last_indexed | 2024-03-09T17:57:34Z |
| publishDate | 2022-11-01 |
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| series | Symmetry |
| spelling | doaj.art-d6b98f4fe9ab47a296e180db1b139be92023-11-24T10:14:03ZengMDPI AGSymmetry2073-89942022-11-011411243810.3390/sym14112438Ulam Stability of Fractional Hybrid Sequential Integro-Differential Equations with Existence and Uniqueness TheoryObaid Algahtani0Department of Mathematics, College of Sciences, King Saud University, P.O. Box 2455, Riyadh 11451, Saudi ArabiaIn this paper, a variety of boundary value problems (BVPs) known as hybrid fractional sequential integro-differential equations (HFSIDs) with two point orders (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi mathvariant="fraktur">p</mi><mo>,</mo><mi mathvariant="fraktur">q</mi></mrow></semantics></math></inline-formula>) are investigated. The uniqueness and existence of the solution are discussed via Banach fixed-point theorems. Certain particular theorems associated with Hyers–Ulam and Hyers–Ulam–Rassias stability to the solution, as well as the uniqueness and existence of the solution of the BVPs are studied. The results are illustrated with some particular examples, and the numerical data are analyzed for confirmation of the results. The results obtained in this work are simple and can easily be applicable to physical systems. Furthermore, symmetry analysis of fractional differential equations and HFSIDs are also presented. This is due to the fact that the aforementioned analysis plays a significant role in both the optimization and qualitative theory of fractional differential equations.https://www.mdpi.com/2073-8994/14/11/2438boundary value problemHFSIDfixed-point theoremHyers–Ulam and Hyers–Ulam–Rassias stability |
| spellingShingle | Obaid Algahtani Ulam Stability of Fractional Hybrid Sequential Integro-Differential Equations with Existence and Uniqueness Theory Symmetry boundary value problem HFSID fixed-point theorem Hyers–Ulam and Hyers–Ulam–Rassias stability |
| title | Ulam Stability of Fractional Hybrid Sequential Integro-Differential Equations with Existence and Uniqueness Theory |
| title_full | Ulam Stability of Fractional Hybrid Sequential Integro-Differential Equations with Existence and Uniqueness Theory |
| title_fullStr | Ulam Stability of Fractional Hybrid Sequential Integro-Differential Equations with Existence and Uniqueness Theory |
| title_full_unstemmed | Ulam Stability of Fractional Hybrid Sequential Integro-Differential Equations with Existence and Uniqueness Theory |
| title_short | Ulam Stability of Fractional Hybrid Sequential Integro-Differential Equations with Existence and Uniqueness Theory |
| title_sort | ulam stability of fractional hybrid sequential integro differential equations with existence and uniqueness theory |
| topic | boundary value problem HFSID fixed-point theorem Hyers–Ulam and Hyers–Ulam–Rassias stability |
| url | https://www.mdpi.com/2073-8994/14/11/2438 |
| work_keys_str_mv | AT obaidalgahtani ulamstabilityoffractionalhybridsequentialintegrodifferentialequationswithexistenceanduniquenesstheory |