In this study, we tackled the issue of insufficient information sharing among small and medium-sized enterprises (SMEs) in supply chain finance (SCF). Blockchain technology (BCT), with its tamper-proof and decentralized nature, offers a viable solution. The adoption of BCT can be viewed as a diffusion process, which we modeled by extending the classic SEIR epidemic framework with Caputo fractional-order derivatives and time-delay effects. We also introduced a nonlinear index to measure potential adopters' sensitivity to information sharing and examined its influence on diffusion speed and adoption scale. Theoretical analysis showed that when the basic reproduction number exceeds one, a unique endemic equilibrium emerges. Moreover, the interplay between time delays and fractional-order memory effects can trigger Hopf bifurcation, leading to oscillatory adoption patterns. Numerical simulations revealed a negative correlation between the fractional order and critical time delay. Importantly, while greater sensitivity to information sharing generally accelerates diffusion and enlarges the final adoption scale under certain conditions, exceeding an optimal threshold may reduce diffusion efficiency. These results suggest that although enhanced information sharing fosters blockchain adoption, it must be carefully managed to avoid adverse outcomes. This study offers theoretical insights and practical guidance for optimizing blockchain promotion strategies in SCF.