On the generalized coupled Hadamard-Gronwall-Bellman-type inequalities with applications to fractional delay systems
[EN] The Gronwall-Bellman inequality is a primary tool for proving various types of stability. For this importance, the present paper focuses on the generalized forms of the well-known Gronwall-Bellman inequality in the context of the Hadamard fractional calculus. We prove and generalize the coupled...
| Autores: | , , |
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| Formato: | artículo |
| Fecha de publicación: | 2025 |
| País: | España |
| Recursos: | Universitat Politècnica de València (UPV) |
| Repositorio: | RiuNet. Repositorio Institucional de la Universitat Politécnica de Valéncia |
| Idioma: | inglés |
| OAI Identifier: | oai:riunet.upv.es:10251/233206 |
| Acesso em linha: | https://riunet.upv.es/handle/10251/233206 |
| Access Level: | acceso abierto |
| Palavra-chave: | Hadamard fractional integral Gronwall-Bellman inequality Coupled system Stability of solutions Existence results |
| Resumo: | [EN] The Gronwall-Bellman inequality is a primary tool for proving various types of stability. For this importance, the present paper focuses on the generalized forms of the well-known Gronwall-Bellman inequality in the context of the Hadamard fractional calculus. We prove and generalize the coupled version of the Hadamard-Gronwall-Bellman inequality and then, generalize its extended form with the sum of two non-decreasing functions. In the sequel, the applicability of these inequalities is established in proving the existence and Ulam-Hyers stability of a Caputo-Hadamard coupled delay system and a Caputo-Hadamard damped initial value problem, which are appeared in population dynamic problems. |
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