@article{Momani2026, 
author = {Shaher Momani and Iqbal H. Jebril and Iqbal M. Batiha and Lina S. Calucag and Anjan Biswas},
title = {Analyzing finite-time convergence for variable-order fractional discrete dynamics in Degn–Harrison reaction–diffusion systems},
year = {2026},
journal = {AIMS Mathematics},
volume = {11},
number = {4},
pages = {12204-12232},
keywords = {finite-time stability, variable-order fractional operators, reaction-diffusion systems, Lyapunov methods, discrete Caputo difference, Mittag-Leffler stability},
url = {https://www.sciopen.com/article/10.3934/math.2026501},
doi = {10.3934/math.2026501},
abstract = {This study presents a novel investigation into finite-time stability (FTS) and synchronization phenomena within a discrete reaction–diffusion system (RDS) governed by variable-order fractional (VOF) operators, inspired by the Degn–Harrison (D–H) model. By employing Caputo-type VOF differences, we model memory effects and time-varying dynamics typical of complex biological and chemical processes. Theoretical contributions include rigorous Lyapunov function (LF)-based criteria for establishing tempered Mittag-Leffler stability (MLS) and global FTS, as well as explicit expressions for the settling time        T          ∗      . A fractional-order (FO) error system is also analyzed, demonstrating that linear coupling ensures finite-time synchronization under variable-order conditions. Extensive numerical simulations confirm the theoretical predictions across various FO profiles    δ  (  t  ) and parameter regimes. These findings bridge discrete fractional modeling with practical control strategies for systems exhibiting hereditary and anomalous diffusion effects.}
}