Generalized UH-stability of a nonlinear fractional coupling ( p 1 , p 2 ) $(\mathcalligra{p}_{1},\mathcalligra{p}_{2})$ -Laplacian system concerned with nonsingular Atangana–Baleanu fractional calculus
Abstract The classical p $\mathcalligra{p}$ -Laplace equation is one of the special and significant second-order ODEs. The fractional-order p $\mathcalligra{p}$ -Laplace ODE is an important generalization. In this paper, we mainly treat with a nonlinear coupling ( p 1 , p 2 ) $(\mathcalligra{p}_{1},...
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| Format: | Article |
| Language: | English |
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SpringerOpen
2023-07-01
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| Series: | Journal of Inequalities and Applications |
| Subjects: | |
| Online Access: | https://doi.org/10.1186/s13660-023-03010-3 |
| _version_ | 1797769315952361472 |
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| author | Kaihong Zhao |
| author_facet | Kaihong Zhao |
| author_sort | Kaihong Zhao |
| collection | DOAJ |
| description | Abstract The classical p $\mathcalligra{p}$ -Laplace equation is one of the special and significant second-order ODEs. The fractional-order p $\mathcalligra{p}$ -Laplace ODE is an important generalization. In this paper, we mainly treat with a nonlinear coupling ( p 1 , p 2 ) $(\mathcalligra{p}_{1},\mathcalligra{p}_{2})$ -Laplacian systems involving the nonsingular Atangana–Baleanu (AB) fractional derivative. In accordance with the value range of parameters p 1 $\mathcalligra{p}_{1}$ and p 2 $\mathcalligra{p}_{2}$ , we obtain sufficient criteria for the existence and uniqueness of solution in four cases. By using some inequality techniques we further establish the generalized UH-stability for this system. Finally, we test the validity and practicality of the main results by an example. |
| first_indexed | 2024-03-12T21:06:11Z |
| format | Article |
| id | doaj.art-965a909d275c485b9729b6cefcffd0a4 |
| institution | Directory Open Access Journal |
| issn | 1029-242X |
| language | English |
| last_indexed | 2024-03-12T21:06:11Z |
| publishDate | 2023-07-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of Inequalities and Applications |
| spelling | doaj.art-965a909d275c485b9729b6cefcffd0a42023-07-30T11:26:59ZengSpringerOpenJournal of Inequalities and Applications1029-242X2023-07-012023111610.1186/s13660-023-03010-3Generalized UH-stability of a nonlinear fractional coupling ( p 1 , p 2 ) $(\mathcalligra{p}_{1},\mathcalligra{p}_{2})$ -Laplacian system concerned with nonsingular Atangana–Baleanu fractional calculusKaihong Zhao0Department of Mathematics, School of Electronics & Information Engineering, Taizhou UniversityAbstract The classical p $\mathcalligra{p}$ -Laplace equation is one of the special and significant second-order ODEs. The fractional-order p $\mathcalligra{p}$ -Laplace ODE is an important generalization. In this paper, we mainly treat with a nonlinear coupling ( p 1 , p 2 ) $(\mathcalligra{p}_{1},\mathcalligra{p}_{2})$ -Laplacian systems involving the nonsingular Atangana–Baleanu (AB) fractional derivative. In accordance with the value range of parameters p 1 $\mathcalligra{p}_{1}$ and p 2 $\mathcalligra{p}_{2}$ , we obtain sufficient criteria for the existence and uniqueness of solution in four cases. By using some inequality techniques we further establish the generalized UH-stability for this system. Finally, we test the validity and practicality of the main results by an example.https://doi.org/10.1186/s13660-023-03010-3Coupling Laplacian systemAB-fractional calculusExistence and uniquenessGeneralized UH-stability |
| spellingShingle | Kaihong Zhao Generalized UH-stability of a nonlinear fractional coupling ( p 1 , p 2 ) $(\mathcalligra{p}_{1},\mathcalligra{p}_{2})$ -Laplacian system concerned with nonsingular Atangana–Baleanu fractional calculus Journal of Inequalities and Applications Coupling Laplacian system AB-fractional calculus Existence and uniqueness Generalized UH-stability |
| title | Generalized UH-stability of a nonlinear fractional coupling ( p 1 , p 2 ) $(\mathcalligra{p}_{1},\mathcalligra{p}_{2})$ -Laplacian system concerned with nonsingular Atangana–Baleanu fractional calculus |
| title_full | Generalized UH-stability of a nonlinear fractional coupling ( p 1 , p 2 ) $(\mathcalligra{p}_{1},\mathcalligra{p}_{2})$ -Laplacian system concerned with nonsingular Atangana–Baleanu fractional calculus |
| title_fullStr | Generalized UH-stability of a nonlinear fractional coupling ( p 1 , p 2 ) $(\mathcalligra{p}_{1},\mathcalligra{p}_{2})$ -Laplacian system concerned with nonsingular Atangana–Baleanu fractional calculus |
| title_full_unstemmed | Generalized UH-stability of a nonlinear fractional coupling ( p 1 , p 2 ) $(\mathcalligra{p}_{1},\mathcalligra{p}_{2})$ -Laplacian system concerned with nonsingular Atangana–Baleanu fractional calculus |
| title_short | Generalized UH-stability of a nonlinear fractional coupling ( p 1 , p 2 ) $(\mathcalligra{p}_{1},\mathcalligra{p}_{2})$ -Laplacian system concerned with nonsingular Atangana–Baleanu fractional calculus |
| title_sort | generalized uh stability of a nonlinear fractional coupling p 1 p 2 mathcalligra p 1 mathcalligra p 2 laplacian system concerned with nonsingular atangana baleanu fractional calculus |
| topic | Coupling Laplacian system AB-fractional calculus Existence and uniqueness Generalized UH-stability |
| url | https://doi.org/10.1186/s13660-023-03010-3 |
| work_keys_str_mv | AT kaihongzhao generalizeduhstabilityofanonlinearfractionalcouplingp1p2mathcalligrap1mathcalligrap2laplaciansystemconcernedwithnonsingularatanganabaleanufractionalcalculus |