Dynamic optimal control of enhancing feedback treatment for a delayed fractional order predator–prey model

2020 ◽  
Vol 554 ◽  
pp. 124136 ◽  
Author(s):  
Chengdai Huang ◽  
Heng Liu ◽  
Xiaoping Chen ◽  
Minsong Zhang ◽  
Ling Ding ◽  
...  
Keyword(s):  
Optimal Control ◽  
Fractional Order ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Prey Model

scholarly journals A predator–prey model involving variable-order fractional differential equations with Mittag-Leffler kernel

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Aziz Khan ◽  
Hashim M. Alshehri ◽  
J. F. Gómez-Aguilar ◽  
Zareen A. Khan ◽  
G. Fernández-Anaya
Keyword(s):  
Fractional Order ◽  
Existence And Uniqueness ◽  
Variable Order ◽  
Fractional Order Systems ◽  
New Approach ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Prey Model ◽  
Fractional Differential ◽  
The Fixed Point Theorem

AbstractThis paper is about to formulate a design of predator–prey model with constant and time fractional variable order. The predator and prey act as agents in an ecosystem in this simulation. We focus on a time fractional order Atangana–Baleanu operator in the sense of Liouville–Caputo. Due to the nonlocality of the method, the predator–prey model is generated by using another FO derivative developed as a kernel based on the generalized Mittag-Leffler function. Two fractional-order systems are assumed, with and without delay. For the numerical solution of the models, we not only employ the Adams–Bashforth–Moulton method but also explore the existence and uniqueness of these schemes. We use the fixed point theorem which is useful in describing the existence of a new approach with a particular set of solutions. For the illustration, several numerical examples are added to the paper to show the effectiveness of the numerical method.

scholarly journals Analysis for fractional‐order predator–prey model with uncertainty

2019 ◽  
Vol 13 (6) ◽  
pp. 277-289 ◽  
Author(s):  
Samayan Narayanamoorthy ◽  
Dumitru Baleanu ◽  
Kalidas Thangapandi ◽  
Shyam Sanjeewa Nishantha Perera
Keyword(s):  
Fractional Order ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Prey Model

A fractional-order predator–prey model with Beddington–DeAngelis functional response and time-delay

2018 ◽  
Vol 27 (2) ◽  
pp. 525-538 ◽  
Author(s):  
Rajivganthi Chinnathambi ◽  
Fathalla A. Rihan ◽  
Hebatallah J. Alsakaji
Keyword(s):  
Time Delay ◽  
Functional Response ◽  
Fractional Order ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Prey Model

Optimal control of a diffusive eco-epidemiological predator–prey model

2020 ◽  
Vol 13 (07) ◽  
pp. 2050065
Author(s):  
Xuebing Zhang ◽  
Guanglan Wang ◽  
Honglan Zhu
Keyword(s):  
Optimal Control ◽  
Semigroup Theory ◽  
Prey Population ◽  
Optimal Controls ◽  
Controlled System ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Prey Model ◽  
The Cost ◽  
Infected Prey

In this study, we investigate the optimal control problem for a diffusion eco-epidemiological predator–prey model. We applied two controllers to this model. One is the separation control, which separates the uninfected prey from the infected prey population, and the other is used as a treatment control to decrease the mortality caused by the disease. Then, we propose an optimal problem to minimize the infected prey population at the final time and the cost cause by the controls. To do this, by the operator semigroup theory we prove the existence of the solution to the controlled system. Furthermore, we prove the existence of the optimal controls and obtain the first-order necessary optimality condition for the optimal controls. Finally, some numerical simulations are carried out to support the theoretical results.

scholarly journals Dynamics of a Fractional-Order Predator-Prey Model with Infectious Diseases in Prey

2019 ◽  
Vol 2 (2) ◽  
pp. 105 ◽  
Author(s):  
Hasan S. Panigoro ◽  
Agus Suryanto ◽  
Wuryansari Muharini Kusumahwinahyu ◽  
Isnani Darti
Keyword(s):  
Infectious Diseases ◽  
Fractional Order ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Prey Model
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