<p>This study develops a Fractional-Order Reaction–Diffusion (FO-RD) model to capture the spatiotemporal dynamics of the adoption of Remote Healthcare Systems (RHS) in geographically isolated regions. By integrating Caputo fractional derivatives (CFDs) into a classical RD framework, the model incorporates memory effects and non-Markovian dynamics that characterize human behavioral responses to healthcare interventions. The model comprises three interacting compartments: unaware population, adopter population, and healthcare need, which evolve through socially driven local reactions and spatial diffusion. Theoretical stability analysis establishes conditions for local and global Mittag-Leffler stability of the equilibrium points. Numerical simulations validate the theoretical results and demonstrate how the FO modulates memory strength in adoption dynamics. Specifically, lower values of the fractional order (stronger memory) lead to slower initial adoption but more sustained long-term adoption. Sensitivity analysis highlights the influence of key parameters such as social contagion rate, external influence, adopter mobility, and relapse rate. The model serves as a quantitative tool for predicting adoption patterns, identifying geographical tipping points, and evaluating policy interventions aimed at enhancing healthcare equity in remote areas.</p>