Fractional spatial diffusion of a biological population model via a new integral transform in the settings of power and Mittag-Leffler nonsingular kernel

The current paper examines some novel and interesting aspects of the fractional biological population model involving the efficacious Atangana-Baleanu fractional derivative operator. It assists us in comprehending the dynamical techniques of population changes in biological population models and generates precise prognostication. This technique correlates with the Elzaki transform method and the homotopy perturbation method. The Elzaki transform is a modification of the classical Fourier Laplace transform. The approximate-analytical solutions of the biological population model are examined using the Elzaki transform homotopy perturbation method (ETHPM). The exact solution of the aforesaid scheme is being investigated in terms of the Mittag-Leffler function. The role of fractional-order on spatial diffusion of a biological population model is demonstrated in two and three-dimensional surface plots. The comparative analysis between exact and numerical solutions reveals the innovative features of the composite fractional derivative in the discussed model. Furthermore, the proposed approach is very powerful, reliable, well-organized, and pragmatic for fractional PDEs and it might be extended to other physical processes.

Automated summary

This paper investigates novel and interesting aspects of the fractional biological population model using the efficacious Atangana-Baleanu fractional derivative operator, providing insight into the dynamical techniques of population changes and generating precise prognostication. The technique correlates with the Elzaki transform method and the homotopy perturbation method, examining approximate-analytical solutions of the model. The role of a fractional-order on spatial diffusion is demonstrated and the innovative features of the composite fractional derivative are revealed through comparative analysis between exact and numerical solutions. The proposed approach is powerful, reliable, well-organized, and pragmatic for fractional PDEs, potentially extendable to other physical processes.