Abstract
In this work, we introduce fractional order predator–prey model with infected predator. First, we prove different mathematical results like existence, uniqueness, non-negativity and boundedness of the solutions of fractional order dynamical system. Further, we investigate the local and global stability of all feasible equilibrium points of the system. Numerical results are illustrated as several examples.
Acknowledgements:
The authors would like to thank the anonymous referees and the editors for making fruitful comments and suggestions in order to improve the quality of the paper. The first author is thankful to UGC(BSR)-Start Up Grant (Grant No. F.30-361/2017(BSR)), University Grants Commission, New Delhi and the DST-FIST (Grant No. SR/FST/MSI-115/2016 (Level-I)), Department of Science and Technology, New Delhi for providing financial support. Third author supported by UGC-BSR Faculty Fellow, University Grants Commission, New Delhi.
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© 2018 Walter de Gruyter GmbH, Berlin/Boston
Articles in the same Issue
- Frontmatter
- Numerical Treatment of the Modified Burgers’ Equation via Backward Differentiation Formulas of Orders Two and Three
- Return Mapping Algorithms (RMAs) for Two-Yield Surface Thermoviscoplastic Models Using the Consistent Tangent Operator
- Synchronization of Multiple Mechanical Oscillators Under Noisy Measurements Signals and Mismatch Parameters
- Nonlinear Wave Modulation in Nanorods Using Nonlocal Elasticity Theory
- Asymptotic Behavior of the Fractional Order three Species Prey–Predator Model
- Continuous Dependence on Data for Solutions of Fractional Extended Fisher–Kolmogorov Equation
- L-stable Explicit Nonlinear Method with Constant and Variable Step-size Formulation for Solving Initial Value Problems
- Weakness and Mittag–Leffler Stability of Solutions for Time-Fractional Keller–Segel Models
- Stability Analysis of Multi-point Boundary Value Problem for Sequential Fractional Differential Equations with Non-instantaneous Impulses
- Existence and Uniqueness of Classical and Mild Solutions of Generalized Impulsive Evolution Equation
- A Collocation Method Based on Jacobi and Fractional Order Jacobi Basis Functions for Multi-Dimensional Distributed-Order Diffusion Equations
- Two-Dimensional Legendre Wavelets for Solving Variable-Order Fractional Nonlinear Advection-Diffusion Equation with Variable Coefficients
Articles in the same Issue
- Frontmatter
- Numerical Treatment of the Modified Burgers’ Equation via Backward Differentiation Formulas of Orders Two and Three
- Return Mapping Algorithms (RMAs) for Two-Yield Surface Thermoviscoplastic Models Using the Consistent Tangent Operator
- Synchronization of Multiple Mechanical Oscillators Under Noisy Measurements Signals and Mismatch Parameters
- Nonlinear Wave Modulation in Nanorods Using Nonlocal Elasticity Theory
- Asymptotic Behavior of the Fractional Order three Species Prey–Predator Model
- Continuous Dependence on Data for Solutions of Fractional Extended Fisher–Kolmogorov Equation
- L-stable Explicit Nonlinear Method with Constant and Variable Step-size Formulation for Solving Initial Value Problems
- Weakness and Mittag–Leffler Stability of Solutions for Time-Fractional Keller–Segel Models
- Stability Analysis of Multi-point Boundary Value Problem for Sequential Fractional Differential Equations with Non-instantaneous Impulses
- Existence and Uniqueness of Classical and Mild Solutions of Generalized Impulsive Evolution Equation
- A Collocation Method Based on Jacobi and Fractional Order Jacobi Basis Functions for Multi-Dimensional Distributed-Order Diffusion Equations
- Two-Dimensional Legendre Wavelets for Solving Variable-Order Fractional Nonlinear Advection-Diffusion Equation with Variable Coefficients