Nonlinear biological population model; computational and numerical investigations

Abstract

This research paper provides precise solutions for nonlinear fractional population biology (FBP) models by implementing the generalized Khater (GK) technique and utilizing Atangana's conformable fractional (ACF) derivative operator. Because people have natural death and a birth rate, we can get demographic information using a model. Many physical features, such as exponential, hyperbolic, and trigonometric functions, were given a mathematical explanation. To get a better understanding of such methods, one should draw them in various ways. Many novel analytical solutions are obtained in distinct formulas, such as rational, hyperbolic, parabolic, etc.Additionally, we use Hamiltonian system properties to confirm the stability of the solutions we get. Finally, the trigonometric- quantic-B- spline (TQBS) scheme tests the accuracy of the obtained solutions through the novel applied analytical method by revealing potential problems and eliminating absolute errors. The power and effectiveness of the two employed analytical and numerical techniques are verified through their performances.