<p>Open channel flow often carries toxic wastes and non-degradable materials as sediments, which negatively impact marine life and water quality. Therefore, monitoring the distribution of suspended sediment concentration (SSC) in open channel flows is of critical importance for effective water resource management. In this study, the time-averaged normalized sediment concentration is treated as a random variable to derive its optimal probability density function (pdf) using the fractional order entropy proposed by Machado. The Lambert <i>W</i> function is employed to derive the pdf under a specified convergence criterion, which is then used to obtain the vertical concentration distribution. To address the computational complexity of determining the Lagrange multipliers and the entropy index in the fractional entropy-based concentration model, a new optimization (minimization) problem is formulated that incorporates the convergence condition. The proposed model is validated using both experimental and field data sets. Additionally, regression and error analyses are conducted to demonstrate the model’s advantages over extant entropy-based probabilistic and classical deterministic models.</p>