<p>This paper presents a novel investigation into the free convective flow of a dusty nanofluid confined between parallel plates, employing the Caputo–Fabrizio fractional derivative model to address a significant gap in existing research. The primary novelty lies in the application of this advanced fractional calculus framework to accurately model the memory and non-local characteristics inherent in such two-phase systems. Exact analytical solutions for the temperature and velocity distributions are derived using a combined approach of Laplace and Finite Sine Fourier Transforms. A parametric study examines the influence of key dimensionless numbers, including Grashof number (Gr), dusty fluid parameter (<i>K</i>), Reynolds number (Re), and fractional parameter (<i>α</i>). The findings reveal that the fractional model offers a superior representation of the physical system compared to classical models; for instance, a specific fractional parameter value (<i>α</i> = 0.5) yields a velocity profile enhancement of approximately 15%. This analysis further shows that increasing <i>α</i> from 0.5 to 1.5 amplifies the nanofluid velocity by up to 20%, and elevating the Grashof number from 2 to 8 results in a roughly 25% velocity increase. Further, this study also explores thermodynamic irreversibility, demonstrating that entropy generation is reduced with higher dusty fluid parameters, while the Bejan number increases, highlighting the dominance of heat transfer irreversibility. The Nusselt number, an indicator of heat transfer rate, is found to reach values as high as 1.810 under certain parametric conditions. These results have direct implications for optimizing thermal performance in engineering applications, such as compact heat exchangers and advanced particle separation technologies. It is concluded that the Caputo–Fabrizio fractional derivative provides a more powerful and accurate tool for predicting the behavior of complex dusty nanofluid flows.</p>