H-U-Type Stability and Numerical Solutions for a Nonlinear Model of the Coupled Systems of Navier BVPs via the Generalized Differential Transform Method
This paper is devoted to generalizing the standard system of Navier boundary value problems to a fractional system of coupled sequential Navier boundary value problems by using terms of the Caputo derivatives. In other words, for the first time, we design a multi-term fractional coupled system of Na...
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| Format: | Article |
| Language: | English |
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MDPI AG
2021-10-01
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| Series: | Fractal and Fractional |
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| Online Access: | https://www.mdpi.com/2504-3110/5/4/166 |
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| author | Shahram Rezapour Brahim Tellab Chernet Tuge Deressa Sina Etemad Kamsing Nonlaopon |
| author_facet | Shahram Rezapour Brahim Tellab Chernet Tuge Deressa Sina Etemad Kamsing Nonlaopon |
| author_sort | Shahram Rezapour |
| collection | DOAJ |
| description | This paper is devoted to generalizing the standard system of Navier boundary value problems to a fractional system of coupled sequential Navier boundary value problems by using terms of the Caputo derivatives. In other words, for the first time, we design a multi-term fractional coupled system of Navier equations under the fractional boundary conditions. The existence theory is studied regarding solutions of the given coupled sequential Navier boundary problems via the Krasnoselskii’s fixed-point theorem on two nonlinear operators. Moreover, the Banach contraction principle is applied to investigate the uniqueness of solution. We then focus on the Hyers–Ulam-type stability of its solution. Furthermore, the approximate solutions of the proposed coupled fractional sequential Navier system are obtained via the generalized differential transform method. Lastly, the results of this research are supported by giving simulated examples. |
| first_indexed | 2024-03-10T04:05:03Z |
| format | Article |
| id | doaj.art-25de45dab64d46c68826969f0b58f179 |
| institution | Directory Open Access Journal |
| issn | 2504-3110 |
| language | English |
| last_indexed | 2024-03-10T04:05:03Z |
| publishDate | 2021-10-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Fractal and Fractional |
| spelling | doaj.art-25de45dab64d46c68826969f0b58f1792023-11-23T08:23:10ZengMDPI AGFractal and Fractional2504-31102021-10-015416610.3390/fractalfract5040166H-U-Type Stability and Numerical Solutions for a Nonlinear Model of the Coupled Systems of Navier BVPs via the Generalized Differential Transform MethodShahram Rezapour0Brahim Tellab1Chernet Tuge Deressa2Sina Etemad3Kamsing Nonlaopon4Department of Medical Research, China Medical University Hospital, China Medical University, Taichung 40447, TaiwanLaboratory of Applied Mathematics, Kasdi Merbah University, Ouargla 30000, AlgeriaDepartment of Mathematics, College of Natural Sciences, Jimma University, Jimma, EthiopiaDepartment of Mathematics, Azarbaijan Shahid Madani University, Tabriz 53751-71379, IranDepartment of Mathematics, Khon Kaen University, Khon Kaen 40002, ThailandThis paper is devoted to generalizing the standard system of Navier boundary value problems to a fractional system of coupled sequential Navier boundary value problems by using terms of the Caputo derivatives. In other words, for the first time, we design a multi-term fractional coupled system of Navier equations under the fractional boundary conditions. The existence theory is studied regarding solutions of the given coupled sequential Navier boundary problems via the Krasnoselskii’s fixed-point theorem on two nonlinear operators. Moreover, the Banach contraction principle is applied to investigate the uniqueness of solution. We then focus on the Hyers–Ulam-type stability of its solution. Furthermore, the approximate solutions of the proposed coupled fractional sequential Navier system are obtained via the generalized differential transform method. Lastly, the results of this research are supported by giving simulated examples.https://www.mdpi.com/2504-3110/5/4/166coupled systemsexistenceGDT-methodnumerical solutionsnavier problemH-U-type stability analysis |
| spellingShingle | Shahram Rezapour Brahim Tellab Chernet Tuge Deressa Sina Etemad Kamsing Nonlaopon H-U-Type Stability and Numerical Solutions for a Nonlinear Model of the Coupled Systems of Navier BVPs via the Generalized Differential Transform Method Fractal and Fractional coupled systems existence GDT-method numerical solutions navier problem H-U-type stability analysis |
| title | H-U-Type Stability and Numerical Solutions for a Nonlinear Model of the Coupled Systems of Navier BVPs via the Generalized Differential Transform Method |
| title_full | H-U-Type Stability and Numerical Solutions for a Nonlinear Model of the Coupled Systems of Navier BVPs via the Generalized Differential Transform Method |
| title_fullStr | H-U-Type Stability and Numerical Solutions for a Nonlinear Model of the Coupled Systems of Navier BVPs via the Generalized Differential Transform Method |
| title_full_unstemmed | H-U-Type Stability and Numerical Solutions for a Nonlinear Model of the Coupled Systems of Navier BVPs via the Generalized Differential Transform Method |
| title_short | H-U-Type Stability and Numerical Solutions for a Nonlinear Model of the Coupled Systems of Navier BVPs via the Generalized Differential Transform Method |
| title_sort | h u type stability and numerical solutions for a nonlinear model of the coupled systems of navier bvps via the generalized differential transform method |
| topic | coupled systems existence GDT-method numerical solutions navier problem H-U-type stability analysis |
| url | https://www.mdpi.com/2504-3110/5/4/166 |
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