In response to increased desertification in Africa due to climate change, understanding the behavior of particulate matter with aerodynamic diameters less than or equal to 2.5 and 10 mu m (PM2.5 and PM10) in the Caribbean is crucial. Fine particles originating from the African dust belt significantly impact the health of the Caribbean population. This study employs a multifractal framework to analyze PM2.5 and PM10 time series data in Puerto Rico from 2000 to 2010, marking the first such investigation in the Caribbean islands. Multifractal Detrended Fluctuation Analysis (MF-DFA) reveals similar multifractal behavior in PM10 and PM2.5 fluctuations, suggesting a shared influence on these pollutants. Hurst exponents of 0.594 for PM10 and 0.642 for PM2.5 indicate long-term persistence in particulate matter behavior. African dust notably influences PM10, displaying slightly greater intermittency. Shuffled and surrogate signal analyses confirm multifractality in PMs time series, representing long-range correlations in small and large fluctuations and broadness in probability density function. The primary contributor to multifractality in PM2.5 is identified as the broadness of the probability density function. Multifractal Detrended Cross-Correlation Analysis (MF-DXA) reveals anti-persistence in cross-correlated multifractal behavior of PMs. These insights enhance the understanding of PM2.5 and PM10 dynamics, aiding predictions of natural occurrences like sand mist and improving health risk management in the Caribbean basin.