<p>In this study, we introduce a novel fuzzy dynamic model for conflicts, incorporating fuzzy theory with fractional-order derivatives and moderation terms. Previous studies developed fuzzy conflict models utilizing differential equations with an external force represented by a sinusoidal function. The contribution of this paper is applying two methods to enhance the sophistication and precision of the existing fuzzy dynamic conflict model. First, we employ fractional-order derivatives to account for memory effects, capturing nuanced changes in conflict dynamics between opposing groups. Second, moderation terms are introduced to observe the interaction between the two groups, enabling self-regulation of conflict by autonomously modulating the degree of change. This makes the proposed model more refined than previous ones, allowing it to simulate real-world conflict scenarios more accurately. By incorporating fractional-order derivatives, the model effectively captures the sensitive rate of change in conflict intensity. This allows for reducing or regulating conflict intensity by incorporating moderation terms that reflect the convergence of opinions or statuses between the two groups. Simulation results confirm that these fractional-order derivatives and moderation terms effectively reduce or regulate conflict levels. This study offers mathematical insights into managing and mitigating conflicts between two groups. Furthermore, the findings can be applied to conflict scenarios between characters in online games, digital twins, or AI and robotics technologies.</p>