![]() Irwin, Memory and mutualism in species sustainability: A time-fractional Lotka-Volterra model with harvesting, Heliyon, 2020, 6(9). Ghafari, Dynamic behavior of a fractional order prey-predator model with group defense, Chaos, Solitons & Fractals, 2020, 134, 109688. Secer, A note on fractional order derivatives and table of fractional derivatives of some special functions, Abstract and applied analysis, Hindawi. El-Saka, Equilibrium points, stability and numerical solutions of fractional-order predator–prey and rabies models, J. Bekiros, Digital currency forecasting with chaotic meta-heuristic bio-inspired signal processing techniques, Chaos, Solitons & Fractals, 2019, 126, 325–336.Į. Hacıoglu˘, Model predictive control of three-axis gimbal system mounted on uav for real-time target tracking under external disturbances, Mech. Daher Okiye, Boundedness and global stability for a predator–prey model with modified Leslie–Gower and Holling-type Ⅱ schemes, Appl. Alam, Risk of disease-selective predation in an infected prey-predator system, Journal of Biological Systems, 2009, 17(1), 111–124. All our observations have been captured in numerical simulation portion and detailed explanations of the outcomes of the numerical simulation have been represented. Also, it has been observed that the corresponding integer order model system may experience saddle-node bifurcation depending upon the change of suitable parameter. The analytical representations of the bifurcation scenarios have been rigorously analyzed. ![]() The higher memory of the interacting species leads to stabilization of the ecological model system whether fading memory has destabilization role in the system dynamics. The fear level makes the system stable around the positive equilibrium point via two consecutive Hopf bifurcations. It is observed that both the fear level and memory bound of the interacting species take crucial part in determining the states of stability of the system dynamics around the co-existence equilibrium point. The states of stability of the possible non-negative equilibrium points have been derived. The well-posedness of the system has been verified analytically. In this article, a Leslie-Gower type predator prey model with fear effect has been proposed and studied in the framework of fractional calculus in Caputo sense.
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