Riccati technique and nonoscillation of damped linear dynamic equations with the conformable derivative on time scales
In this study, we investigate the use of damped linear dynamic equations with the conformable derivative on time scales to provide sufficient conditions to guarantee nonoscillation for nontrivial solutions of both ordinary differential and discrete equations. The nonoscillation theorem is proven usi...
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| Format: | Article |
| Language: | English |
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Elsevier
2025-02-01
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| Series: | Results in Applied Mathematics |
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| Online Access: | http://www.sciencedirect.com/science/article/pii/S2590037425000172 |
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| author | Kazuki Ishibashi |
| author_facet | Kazuki Ishibashi |
| author_sort | Kazuki Ishibashi |
| collection | DOAJ |
| description | In this study, we investigate the use of damped linear dynamic equations with the conformable derivative on time scales to provide sufficient conditions to guarantee nonoscillation for nontrivial solutions of both ordinary differential and discrete equations. The nonoscillation theorem is proven using the Riccati technique, and we provide four examples to explain nonoscillation. The four examples include the damped Euler-type dynamic equation on a time scale, the q-difference equation, and the forward difference and ordinary differential equations with periodic coefficients. In particular, the ordinary differential equation with periodic coefficients is inspired by Whittaker–Hill’s equation, which has applications in the theory of internal rotation in the hydrogen peroxide molecule. |
| format | Article |
| id | doaj-art-a53e289bfe9f406da32c3a543f10c5f8 |
| institution | DOAJ |
| issn | 2590-0374 |
| language | English |
| publishDate | 2025-02-01 |
| publisher | Elsevier |
| record_format | Article |
| series | Results in Applied Mathematics |
| spelling | doaj-art-a53e289bfe9f406da32c3a543f10c5f82025-08-20T02:56:51ZengElsevierResults in Applied Mathematics2590-03742025-02-012510055310.1016/j.rinam.2025.100553Riccati technique and nonoscillation of damped linear dynamic equations with the conformable derivative on time scalesKazuki Ishibashi0Department of Electrical Systems Engineering, Hiroshima Institute of Technology, 2-1-1 Miyake, Saeki-ku, Hiroshima 731-5193, JapanIn this study, we investigate the use of damped linear dynamic equations with the conformable derivative on time scales to provide sufficient conditions to guarantee nonoscillation for nontrivial solutions of both ordinary differential and discrete equations. The nonoscillation theorem is proven using the Riccati technique, and we provide four examples to explain nonoscillation. The four examples include the damped Euler-type dynamic equation on a time scale, the q-difference equation, and the forward difference and ordinary differential equations with periodic coefficients. In particular, the ordinary differential equation with periodic coefficients is inspired by Whittaker–Hill’s equation, which has applications in the theory of internal rotation in the hydrogen peroxide molecule.http://www.sciencedirect.com/science/article/pii/S2590037425000172NonoscillationDynamic equationsConformable derivativeRiccati techniqueTime scale |
| spellingShingle | Kazuki Ishibashi Riccati technique and nonoscillation of damped linear dynamic equations with the conformable derivative on time scales Results in Applied Mathematics Nonoscillation Dynamic equations Conformable derivative Riccati technique Time scale |
| title | Riccati technique and nonoscillation of damped linear dynamic equations with the conformable derivative on time scales |
| title_full | Riccati technique and nonoscillation of damped linear dynamic equations with the conformable derivative on time scales |
| title_fullStr | Riccati technique and nonoscillation of damped linear dynamic equations with the conformable derivative on time scales |
| title_full_unstemmed | Riccati technique and nonoscillation of damped linear dynamic equations with the conformable derivative on time scales |
| title_short | Riccati technique and nonoscillation of damped linear dynamic equations with the conformable derivative on time scales |
| title_sort | riccati technique and nonoscillation of damped linear dynamic equations with the conformable derivative on time scales |
| topic | Nonoscillation Dynamic equations Conformable derivative Riccati technique Time scale |
| url | http://www.sciencedirect.com/science/article/pii/S2590037425000172 |
| work_keys_str_mv | AT kazukiishibashi riccatitechniqueandnonoscillationofdampedlineardynamicequationswiththeconformablederivativeontimescales |