Variable Fractional-Order Reaction-Diffusion System for Edge Preservation in Biomedical Imaging

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.