Analytical Computational Scheme for Multivariate Nonlinear Time-Fractional Generalized Biological Population Model

Abstract

This work provides exact and analytical approximate solutions for a non-linear time-fractional generalized biology population model (FGBPM) with suitable initial data under the time-Caputo fractional derivative, in view of a novel effective and applicable scheme, based upon elegant amalgamation between the Laplace transform operator and the generalized power series method. The solution form obtained by the proposed algorithm of considered FGBPM is an infinite multivariable convergent series toward the exact solutions for the integer fractional order. Some applications of the posed model are tested to confirm the theoretical aspects and highlight the superiority of the proposed scheme in predicting the analytical approximate solutions in closed forms compared to other existing analytical methods. Associated figure representations and the results are displayed in different dimensional graphs. Numerical analyses are performed, and discussions regarding the errors and the convergence of the scheme are presented. The simulations and results report that the proposed modern scheme is, indeed, direct, applicable, and effective to deal with a wide range of non-linear time multivariable fractional models.