Identyfikatory
Warianty tytułu
Języki publikacji
Abstrakty
In this paper, a time-fractional host-parasitoid dynamics which is regarded as a new variant of the novel Nicholson-Bailey model is considered in the sense of the Caputo operator. The model equation is examined for linear stability analysis to guide in ensuring the best choice of parameters when simulating the full dynamical system. Furthermore, this work provides a suitable numerical technique for the approximation of the Caputo fractional derivative with order ρ ∈ (0, 1]. To explore the dynamic richness of the model, numerical results are provided for different values of α.
Rocznik
Tom
Strony
79--90
Opis fizyczny
Bibliogr. 25 poz., rys.
Twórcy
autor
- Department of Mathematical Sciences, Federal University of Technology PMB 704, Akure, Ondo State, Nigeria
- Institute for Groundwater Studies, Faculty of Natural and Agricultural Sciences University of the Free State Bloemfontein 9300, South Africa
autor
- Department of Mathematics and Applied Mathematics, University of Pretoria, Pretoria 002, South Africa
Bibliografia
- [1] Murray, J.D. (1989). Mathematical Biology. Berlin: Springer.
- [2] Kumar, K., Pandey, R.K., & Sharma, S. (2017). Comparative study of three numerical schemes for fractional integro-differential equations. Journal of Computational and Applied Mathematics, 315, 287-302.
- [3] Kumar, K., Pandey, R.K., & Sharma, S. (2019). Approximations of fractional integrals and Caputo derivatives with application in solving Abel’s integral equations. Journal of King Saud University-Science, 31, 692-700.
- [4] Kumar, K., Pandey, R.K., & Sultana, F. (2021). Numerical schemes with convergence for generalized fractional integro-differential equations. Journal of Computational and Applied Mathematics, 388, 113318.
- [5] Yadav, S., Pandey, R.K., & Shukla, A.K. (2019). Numerical approximations of Atangana-Baleanu Caputo derivative and its application. Chaos, Solitons and Fractals, 118, 58-64.
- [6] May, R.M., Hassell, M.P., Anderson, R.M., & Tonkyn, D.W. (1981). Density dependence in host-parasitoid models. Journal of Animal Ecology, 50(3), 855-865.
- [7] Podlubny, I. (1999). Fractional Differential Equations. San Diego, CA: Academic Press.
- [8] Petrás, I. (2011). Fractional-Order Nonlinear Systems: Modeling, Analysis and Simulation. Berlin: Springer.
- [9] Owolabi, K.M., & Atangana, A. (2019). Numerical Methods for Fractional Differentiation. Singapore: Springer.
- [10] Owolabi, K.M., Karaagac, B., & Baleanu, D. (2021). Pattern formation in superdiffusion predator-prey-like problems with integer- and noninteger-order derivatives. Mathematical Methods in the Applied Sciences, 44, 4018-4036.
- [11] Karaagac, B. (2018). Analysis of the cable equation with non-local and non-singular kernel fractional derivative. The European Physical Journal Plus, 133, 2, 1-9.
- [12] Karaagac, B. (2019). A study on fractional Klein Gordon equation with non-local and non-singular kernel. Chaos, Solitons & Fractals, 126, 218-229.
- [13] Karaagac, B. (2019). New exact solutions for some fractional order differential equations via improved sub-equation method. Discrete & Continuous Dynamical Systems-S, 12(3), 447-454.
- [14] Karaagac, B. (2019). Two step Adams Bashforth method for time fractional Tricomi equation with non-local and non-singular Kernel. Chaos, Solitons & Fractals, 128, 234-241.
- [15] Karaagac, B., & Owolabi, K.M. (2021). Numerical analysis of polio model: A mathematical approach to epidemiological model using derivative with Mittag-Leffler Kernel. Mathematical Methods in the Applied Sciences, DOI: 10.1002/mma.7607.
- [16] Samko, S., Kilbas, A., & Marichev, O.(1993). Fractional Integrals and derivatives: Theory and Applications. Amsterdam: Gordon and Breach.
- [17] Atangana, A., & Baleanu, D. (2016), New fractional derivatives with nonlocal and non-singular kernel: Theory and application to heat transfer model. Thermal Science, 20, 763-769.
- [18] Kilbas, A.A., Srivastava, H.M., & Trujillo, J.J. (2006). Theory and Applications of Fractional Differential Equations. Netherlands, Elsevier.
- [19] Jang, S.R.-J., & Yu, J.L. (2006). A discrete-time host-parasitoid model. Proceedings of the Conference on Differential and Difference Equations and Applications. Hindawi Publishing Corporation, 451-455.
- [20] Doha, E.H., Bhrawy, A.H., & Ezz-Eldien, S.S. (2011). A Chebyshev spectral method based on operational matrix for initial and boundary value problems of fractional order. Comput. Math. Appl., 62, 2364-2373.
- [21] Owolabi, K.M. (2021). Robust synchronization of chaotic fractional-order systems with shifted Chebyshev spectral collocation method. Journal of Applied Analysis, DOI: 10.1515/jaa-2021-2053.
- [22] Li, C., & Zeng, F. (2013). The finite difference methods for fractional ordinary differentia equations. Numerical Functional Analysis and Optimization, 34, 149-179.
- [23] Diethelm, K., Ford, N.J., & Freed, A.D. (2004). Detailed error analysis for a fractional Adams method. Numer. Algorithms, 36, 31-52.
- [24] Nicholson, A.J., & Bailey, V.A. (1935). The balance of animal populations, part 1. Proc. of Zoological Society of London, 3, 551-598.
- [25] Qureshi, M.N, Khan, A.Q., & Din, Q. (2014). Asymptotic behavior of a Nicholson-Bailey model. Advances in Difference Equations, 62, 1-11.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-3289a23b-f2ff-4f9e-aec0-3ff4841a50b8