Advanced Mathematical Models & Applications

In many environmental, economic, and medical systems, population dynamics research and population development prediction depend heavily on the application of biology and population equations. These applications are based on a system of mathematical equations that simulate interactions between people in a population as well as biological population development. In the paper we present analytical and numerical solutions to the nonlinear fractional biological population equation (NFBPE) with the fractional derivative Atangana Baleanu (FDAB) using the Kamal Adomian decomposition method (KADM) and the Maple soft and MATLAB. In addition. The considered equation describes diffusion in the nonlinear biological population processes. The paper discusses the existence, uniqueness, and convergence of the solution of this equation. In the end, the method effectively solved the equation and we obtained new and satisfactory results.