Abstract

This study applied the ZZ transformation and the new iterative transform technique to obtain a fascinating explicit pattern for outcomes of the biological population model. It makes important projections and helps us understand the dynamical method of demographic fluctuations in biological population models. Additionally, ZZ transforms combine various other transformations that already exist. We used a complex fractional transformation to deal with a fractional partial differential equation and a new iterative transform approach to study the nonlinear equations in examine the closed form solutions. In mathematics, the number of equations and their solutions that have been discovered and associated with different innovative properties of the proposed model. A variety of images and tabulations are provided to provide extra context for these notions. The suggested technique accuracy and efficiency imply that it can be applied to a wide range of nonlinear evolutionary problems.