A mathematical study of a crop-pest model with the Caputo fractional-order derivative

  • Abdennasser Chekroun Laboratoire d'Analyse Nonlinéaire et Mathématiques Appliquées, University of Tlemcen, Tlemcen 13000, Algeria
  • Mohamed Helal Biomathamatics Laboratory, University Djillali Liabes of Sidi Bel Abbes, Algeria, 22000
  • Dibyendu Sekhar Mandal Amity School of Applied Sciences, Amity University Maharashtra, Mumbai-Pune Expressway, Bhatan, Panvel, Mumbai 410206, India
  • Abdelkader Lakmeche Biomathematics Laboratory, Univ. Sidi Bel-Abbes, P.B. 89, 22000, Algeria
  • El Arbi Miloudi Biomathematics Laboratory, Univ. Sidi Bel-Abbes, P.B. 89, 22000, Algeria

Abstract

The work is deals with the basic results of a fractional order predator-prey system with harvesting. More precisely, crop-pest interactions were studied. Mathematical results like existence, uniqueness and positivity of the solutions are derived. It is shown that the fractional order system undergoes a possible Hopf-bifuracation at the interior equilibrium point. Local and Global stability of the system have been found under some parametric condition. Further an efficient numerical technique (Adams-Bashforth-Moulton method) have been illustrated for better understanding of the dynamics of the systems. In our investigation, the fractional operator is understood in the Caputo sense.

Published
2022-11-20