Abstract
In this research, we develop a new analytical technique based on the Elzaki transform (ET) to solve the fractional-order biological population model (FBPM) with initial and boundary conditions (ICs and BCs). This approach can be used to locate both the closed approximate solution and the exact solution of a differential equation. The usefulness and validity of this strategy for managing the solution of FBPM are demonstrated using a few real-world scenarios. The dependability of the suggested strategy is also shown using a table and a few graphs. The approximate solutions that were achieved and the convergence analysis are shown in numerical simulations in a range of fractional orders. From the numerical simulations, it can be seen that the population density increases with increasing fractional order, whereas the population density drops with decreasing fractional order.