@article{Etemad2025, 
author = {Sina Etemad and Ali Akgül and J. Alberto Conejero},
title = {On the generalized coupled Hadamard-Gronwall-Bellman-type inequalities with applications to fractional delay systems},
year = {2025},
journal = {AIMS Mathematics},
volume = {10},
number = {11},
pages = {27954-27984},
keywords = {Hadamard fractional integral, Gronwall-Bellman inequality, coupled system, stability of solutions, existence results},
url = {https://www.sciopen.com/article/10.3934/math.20251228},
doi = {10.3934/math.20251228},
abstract = {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.}
}