On semi analytical and numerical simulations for a mathematical biological model; the time-fractional nonlinear Kolmogorov–Petrovskii–Piskunov (KPP) equation

Abstract

Abstract Through five latest numerical schemes (Adomian decomposition (AD), El Kalla (EK), cubic B - spline (CBS), expanded Cubic B-Spline (ECBS), exponential cubic B - spline (ExCBS), this manuscript examines semi-analytical and numerical solutions of the time-fractional nonlinear Kolmogorov–Petrovskii–Piskunov (KPP) equation. Using the Caputo–Fabrizio fractional derivative and expanded Riccati - expansion process in Hamed et al.(2020) [1], developed computational solutions are investigated to determine the sufficient conditions for the implementation of the above-suggested schemes. In combustion theory, mathematical biology, and other study fields, the quasi-linear model is parabolic in simulating specific reaction-diffusion systems. The model’s solution represents the proliferation of a favored gene, and moving waves are pursued by nonlinear interaction. By measuring the absolute error between the exact and numerical solutions, the obtained numerical solutions’ consistency is examined. To explain the correspondence between the exact and numerical solutions, several sketches are given.