A fractal-fractional-order modified Predator-Prey mathematical model with immigrations

被引：40
作者：
Ali, Zeeshan [1 ]
Rabiei, Faranak [1 ]
Hosseini, Kamyar [2 ]
机构：
[1] Monash Univ Malaysia, Sch Engn, Subang Jaya 47500, Selangor, Malaysia
[2] Near East Univ TRNC, Dept Math, Mersin, Turkiye
来源：
MATHEMATICS AND COMPUTERS IN SIMULATION | 2023年 / 207卷
关键词：
Modified predator-prey model; Fractal-fractional differential equation; Existence theory; Hyers-Ulam stability; Adam-Bashforth method; ECO-EPIDEMIOLOGIC MODEL; STABILITY ANALYSIS; CALCULUS; DISEASE;
D O I：
10.1016/j.matcom.2023.01.006
中图分类号：
TP39 [计算机的应用];
学科分类号：
081203 ; 0835 ;
摘要：
This manuscript aims to study a modified predator-prey model's existence, stability, and dynamics under the newly developed fractal-fractional order operator in the Caputo-Fabrizio sense. The existence theory of the proposed model carries out through the Leray-Schauder alternative and sufficient conditions for stability are established using the classical technique of nonlinear functional analysis. The numerical results are obtained by the fractal-fractional Adam-Bashforth method in the Caputo-Fabrizio sense. The numerical results show that small immigrations invoke stable convergence in the predator-prey ecosystem. This means that a small number of sporadic immigrants can stabilize natural predator-prey populations. (c) 2023 International Association for Mathematics and Computers in Simulation (IMACS). Published by Elsevier B.V. All rights reserved.
引用
收藏
页码：466 / 481
页数：16
相关论文
共 44 条
[1]   Existence theory and numerical analysis of three species prey-predator model under Mittag-Leffler power law [J].
Abdo, Mohammed S. ;
Panchal, Satish K. ;
Shah, Kamal ;
Abdeljawad, Thabet .
ADVANCES IN DIFFERENCE EQUATIONS, 2020, 2020 (01)
[2]   Fractal-fractional mathematical modeling and forecasting of new cases and deaths of COVID-19 epidemic outbreaks in India [J].
Abdulwasaa, Mansour A. ;
Abdo, Mohammed S. ;
Shah, Kamal ;
Nofal, Taher A. ;
Panchal, Satish K. ;
Kawale, Sunil V. ;
Abdel-Aty, Abdel-Haleem .
RESULTS IN PHYSICS, 2021, 20
[3]   Interpretation and Dynamics of the Lotka-Volterra Model in the Description of a Three-Level Laser [J].
Aboites, Vicente ;
Bravo-Aviles, Jorge Francisco ;
Garcia-Lopez, Juan Hugo ;
Jaimes-Reategui, Rider ;
Huerta-Cuellar, Guillermo .
PHOTONICS, 2022, 9 (01)
[4]   A fractional-order mathematical model for COVID-19 outbreak with the effect of symptomatic and asymptomatic transmissions [J].
Ali, Zeeshan ;
Rabiei, Faranak ;
Rashidi, Mohammad M. ;
Khodadadi, Touraj .
EUROPEAN PHYSICAL JOURNAL PLUS, 2022, 137 (03)
[5]   A Semianalytical Approach to the Solution of Time-Fractional Navier-Stokes Equation [J].
Ali, Zeeshan ;
Nia, Shayan Naseri ;
Rabiei, Faranak ;
Shah, Kamal ;
Tan, Ming Kwang .
ADVANCES IN MATHEMATICAL PHYSICS, 2021, 2021
[6]   Qualitative analysis of fractal-fractional order COVID-19 mathematical model with case study of Wuhan [J].
Ali, Zeeshan ;
Rabiei, Faranak ;
Shah, Kamal ;
Khodadadi, Touraj .
ALEXANDRIA ENGINEERING JOURNAL, 2021, 60 (01) :477-489
[7]   MATHEMATICAL ANALYSIS OF COUPLED SYSTEMS WITH FRACTIONAL ORDER BOUNDARY CONDITIONS [J].
Ali, Zeeshan ;
Shah, Kamal ;
Zada, Akbar ;
Kumam, Poom .
FRACTALS-COMPLEX GEOMETRY PATTERNS AND SCALING IN NATURE AND SOCIETY, 2020, 28 (08)
[8]   Ulam stability results for the solutions of nonlinear implicit fractional order differential equations [J].
Ali, Zeeshan ;
Zada, Akbar ;
Shah, Kamal .
HACETTEPE JOURNAL OF MATHEMATICS AND STATISTICS, 2019, 48 (04) :1092-1109
[9]   On Ulam's Stability for a Coupled Systems of Nonlinear Implicit Fractional Differential Equations [J].
Ali, Zeeshan ;
Zada, Akbar ;
Shah, Kamal .
BULLETIN OF THE MALAYSIAN MATHEMATICAL SCIENCES SOCIETY, 2019, 42 (05) :2681-2699
[10]   Redefined Extended Cubic B-Spline Functions for Numerical Solution of Time-Fractional Telegraph Equation [J].
Amin, Muhammad ;
Abbas, Muhammad ;
Baleanu, Dumitru ;
Iqbal, Muhammad Kashif ;
Riaz, Muhammad Bilal .
CMES-COMPUTER MODELING IN ENGINEERING & SCIENCES, 2021, 127 (01) :361-384
12345