@article{Zhang2026, 
author = {Haonan Zhang and Zidi Zhao and Qixiang Dong},
title = {Asymptotic properties of solutions to Caputo-Hadamard fractional differential equations},
year = {2026},
journal = {AIMS Mathematics},
volume = {11},
number = {6},
pages = {16983-17008},
keywords = {logarithmic Mittag-Leffler stability, Lyapunov's first method, Mittag-Leffler functions, Caputo-Hadamard fractional differential equation},
url = {https://www.sciopen.com/article/10.3934/math.2026695},
doi = {10.3934/math.2026695},
abstract = {This paper investigates the stability properties of Caputo-Hadamard fractional differential equations. We first analyze the asymptotic behavior and rigorously prove a specific convergence rate for these equations. Then, a novel stability criterion called logarithmic Mittag-Leffler stability is proposed. By employing the fixed-point theorem in an innovative Banach space equipped with a designed weighted norm, we demonstrate that when the linearization spectrum of the Caputo-Hadamard fractional differential equation lies within a prescribed sector, the equilibrium point of the equation exhibits logarithmic Mittag-Leffler stability. This result leads to a version of Lyapunov's first method for Caputo-Hadamard fractional differential equations, demonstrating its stability in the presence of logarithmic memory.}
}