Robust QLM-SCFTK matrix approach applied to a biological population model of fractional order considering the carrying capacity

Abstract

Two effective and accurate matrix collocation techniques based on novel generalized shifted Chebyshev functions of the third kind (GSCFTK) are presented to examine the approximate solutions of a fractional-order population model considering the impact of carrying capacity. The fractional operator in the Liouville-Caputo sense is considered. The first direct technique is called the GSCFTK matrix procedure whereas the second one relied on the quasilinearization method and the GSCFTK matrix collocation strategy is called QLM-GSCFTK. In both approaches, the nonlinear population model is transformed into an algebraic system of equations. The resulting matrix equation is nonlinear in the first approach while is linear in the latter one, which is more efficient than the direct matrix method. The convergence analysis of the new generalized bases is established. To testify the robustness and effectiveness of the presented techniques, various numerical simulations are performed using diverse fractional orders. The results prove the applicability of the presented techniques of providing accurate results in comparison to other available numerical models and can be extended to other similar biological problems. Results also show that the numerical schemes are robust.

The Reaction–Diffusion Models in Biomedicine: Highly Accurate Calculations via a Hybrid Matrix Collocation Algorithm

“…Thus, we have to solve a sequence of linearized submodels rather than a single nonlinear model. The wide range of applicability of the QLM to diverse initial and boundary value problems has been shown by many researchers; we refer for comparison [38][39][40].…”