On the existence, uniqueness and computational analysis of a fractional order spatial model for the squirrel population dynamics under the Atangana-Baleanu-Caputo operator

2021;
: pp. 432–443
https://doi.org/10.23939/mmc2021.03.432
Received: April 25, 2021
Accepted: May 19, 2021
1
Department of Mathematics, Faculty of Science, Ekiti State University
2
Department of Mathematics, Faculty of Science, Ekiti State University
3
Department of Mathematics, Faculty of Physical Science, University of Ilorin

In this paper, we examine the fractional order analysis of a diffusion competition spatial model describing the interactions between the externally introduced grey and local red squirrel under the Atangana-Baleanu-Caputo (ABC) sense.  Also, we establish the existence and uniqueness analysis of the fractional order spatial model of the squirrel population dynamics, while the numerical computation of the fractional order spatial model is carried out using the two dimensional Fractional Order Differential Transform Method (FODTM).  Simulations of the variables of the model reveal that as the system evolves, the grey squirrels increase in density with increase in time, while the red squirrels decrease in density with increase in time.  Also the simulations show that the FODTM is efficient and convergent with low computational cost.

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Mathematical Modeling and Computing, Vol. 8, No. 3, pp. 432–443 (2021)