In this paper, the modeling of the dynamics of a fish population through the use of fractional differential equations is explored, with particular attention to ecological applications in changing environmental conditions. The classical logistic model of population growth is studied as a special case, providing a baseline for understanding more complex ecological scenarios. The research covers the Grünwald-Letnikov and Adams-Bashforth-Moulton methods for numerical analysis, which illustrate the dependence of the population growth rate on the order of the fractional derivative. The results of applying numerical methods were compared with those obtained using Picard’s method of successive approximations. It is demonstrated that with smaller values of the order, the growth rate decreases, and as the order approaches one, the model converges to the classical logistic model. The findings obtained confirm that the use of fractional derivatives allows for the consideration of long-term memory effects, ecological delays, and non-local interactions in population evolution, which are crucial for understanding real ecosystem behavior. The developed model can be utilized to forecast real-world population processes, such as the behavior of fish populations when faced with environmental changes, including global warming impacts, anthropogenic disturbances, and ecosystem regime shifts, providing valuable insights for sustainable fisheries management and biodiversity conservation efforts in aquatic ecosystems.