International Journal of Analysis and Applications | 2026
Authors: Anakira N.; Jebril I.H.; Ogilat O.; Batiha I.M.; Sasa T.; Malkawi A.A.M.
DOI: 10.28924/2291-8639-24-2026-23
Journal: International Journal of Analysis and Applications
Year: 2026
Publisher: Etamaths Publishing
Document Type: Article
Open Access: All Open Access; Gold Open Access
Cited by: 6
This paper introduces a novel variable fractional-order reaction-diffusion system (VFO-RDs) to model anisotropic diffusion for edge preservation in biomedical imaging. By leveraging the Caputo nabla variable fractional-order difference operator, the proposed model captures the memory-dependent nature of biological tissues. We establish sufficient conditions for tempered Mittag-Leffler stability (MLS) of the equilibrium point using Lyapunov functions (LFs) and Lipschitz-type bounds on the nonlinear reaction term. Eigenvalue-based constraints on the discrete Laplacian guar-antee contractive dynamics. Numerical simulations in both 1D and 2D domains demonstrate the edge-preserving capa-bilities of the method under various fractional-order (FO) scenarios. The results confirm that the proposed framework effectively maintains critical spatial features and improves stability, providing a viable tool for advanced biomedical image analysis. © 2026 the author(s).
anisotropic diffusion; biomedical imaging; Caputo nabla difference; Mittag-Leffler stability; reaction-diffusion system; Variable fractional-order