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...

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Detalhes bibliográficos
Autores: Etemad, Sina, Akgül, Ali, Conejero, J. Alberto|||0000-0003-3681-7533
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
Descrição
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.