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Modelling and simulation of a dynamical system with the Atangana-Baleanu fractional derivative

  • Kolade M. OwolabiEmail author
Regular Article
Part of the following topical collections:
  1. Focus Point on Modelling Complex Real-World Problems with Fractal and New Trends of Fractional Differentiation

Abstract.

In this paper, we model an ecological system consisting of a predator and two preys with the newly derived two-step fractional Adams-Bashforth method via the Atangana-Baleanu derivative in the Caputo sense. We analyze the dynamical system for correct choice of parameter values that are biologically meaningful. The local analysis of the main model is based on the application of qualitative theory for ordinary differential equations. By using the fixed point theorem idea, we establish the existence and uniqueness of the solutions. Convergence results of the new scheme are verified in both space and time. Dynamical wave phenomena of solutions are verified via some numerical results obtained for different values of the fractional index, which have some interesting ecological implications.

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Copyright information

© Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Institute for Groundwater Studies, Faculty of NaturalAgricultural Sciences University of the Free StateBloemfonteinSouth Africa
  2. 2.Department of Mathematical SciencesFederal University of TechnologyOndo StateNigeria

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