Some stability results for the fractional differential equations with two delays
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866912960910196736 |
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| author | Dutta, Pragati Bhalekar, Sachin |
| author_facet | Dutta, Pragati Bhalekar, Sachin |
| contents | This paper investigates the stability properties of a nonlinear fractional differential equation with two discrete delays and a delay-dependent coefficient. Such equations arise in various biological and control systems where temporal delays influence feedback mechanisms. In the first case, we set one of the delays to zero and analyzed the resulting system. We then extended the study to a more general case where both delays are allowed to vary. We derive delay-independent stability conditions using linearization, characteristic equations, and bifurcation theory, along with complete theoretical proofs. The results are validated through numerical simulations and stability diagrams. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_21937 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Some stability results for the fractional differential equations with two delays Dutta, Pragati Bhalekar, Sachin Dynamical Systems 34K20, 34K18 37C75 37C75, 34K18, This paper investigates the stability properties of a nonlinear fractional differential equation with two discrete delays and a delay-dependent coefficient. Such equations arise in various biological and control systems where temporal delays influence feedback mechanisms. In the first case, we set one of the delays to zero and analyzed the resulting system. We then extended the study to a more general case where both delays are allowed to vary. We derive delay-independent stability conditions using linearization, characteristic equations, and bifurcation theory, along with complete theoretical proofs. The results are validated through numerical simulations and stability diagrams. |
| title | Some stability results for the fractional differential equations with two delays |
| topic | Dynamical Systems 34K20, 34K18 37C75 37C75, 34K18, |
| url | https://arxiv.org/abs/2509.21937 |