Existence theory and numerical analysis of three species prey–predator model under Mittag-Leffler power law

• Main Authors: Mohammed S. Abdo, Satish K. Panchal, Kamal Shah, Thabet Abdeljawad
• Format: Article
• Language: English
• Published: SpringerOpen 2020-05-01
• Series: Advances in Difference Equations
• Subjects: Atangana–Baleanu and Caputo derivative; Existence and stability theory; Adams Bashforth method; Fixed point theorem
• Online Access: http://link.springer.com/article/10.1186/s13662-020-02709-7

Abstract In this manuscript, the fractional Atangana–Baleanu–Caputo model of prey and predator is studied theoretically and numerically. The existence and Ulam–Hyers stability results are obtained by applying fixed point theory and nonlinear analysis. The approximation solutions for the considered model are discussed via the fractional Adams Bashforth method. Moreover, the behavior of the solution to the given model is explained by graphical representations through the numerical simulations. The obtained results play an important role in developing the theory of fractional analytical dynamic of many biological systems.