Convergence and stability analysis of a novel iteration method for fractional biological population equation

We put into action new analytical technique for solving nonlinear fractional partial differential equations arising in biological population dynamics system. We present in details the stability, the convergence, and the uniqueness analysis by constructing a suitable Hilbert space. Some exact analytical solutions are given, and a quantity of properties gives you an idea about signs of biologically practical reliance on the parameter values. The regularity of this course of action and the diminution in computations confer a wider applicability. In all examples, in the limit of infinitely, many terms of the series solution yield the exact solution.