A Fractional Order Delay Differential Model for Survival of Red Blood Cells in an Animal: Stability Analysis

Santqshi Panigrahi; Sunita Chand

doi:10.2478/tmmp-2021-0034

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A Fractional Order Delay Differential Model for Survival of Red Blood Cells in an Animal: Stability Analysis

Tatra Mountains Mathematical Publications

Volume 80 (2021): Issue 3 (December 2021)

By: Santqshi Panigrahi and Sunita Chand

Open Access

|Jan 2022

Abstract

In this paper, we analyse stability of survival of red blood cells in animal fractional order model with time delay. Results have been illustrated by numerical simulations.

References

[1] PODLUBNÝ, I.: Fractional Differential Equations. (An introduction to fractional derivatives, fractional differential equations, to methods of their solution and some of their applications). In: Mathematics in Science and Engineering, Vol. 198. Academic Press, Inc., San Diego, CA, 1999.
Search in Google Scholar Back to article
[2] SAMKO, S. G.—KILBAS, A. A.—MARICHEV, O.I.: Fractional Integrals and Derivatives: Theory and Applications. Gordon and Breach Science Publishers, Yverdon, 1993.
Search in Google Scholar Back to article
[3] WAŻEWSKA-CZYŻEWSKA, M.—LASOTA, A.: Mathematical problems of the dynamics of a system of red blood cells. Mat. Stos. 6 (1976), no. 3, 23–40. (In Polish)
Search in Google Scholar Back to article
[4] GYŐRI, I.—LADAS, G.: Oscillation Theory of Delay Differential Equation: With Applications. In: Oxford Mathematical Monographs. Oxford Science Publications. The Clarendon Press, Oxford University Press, New York, 1991.
Search in Google Scholar Back to article
[5] SONG, Y.—WEI, J.—YUAN, Y.: Bifurcation analysis on a survival red blood cells model, J. Math. Anal. Appl. 316 (2006), 459–471.10.1016/j.jmaa.2005.04.051
Search in Google Scholar Back to article
[6] FAN, D.—WEI, J.: Bifurcation analysis of discrete survival red blood cells model, Commun Nonlinear Sci. Numer. Simul. 14 (2009), no. 8, 3358–3368.
Search in Google Scholar Back to article
[7] SONG, Y.: Positive periodic solutions of a periodic survival red blood cell model, Appl. Anal. 84 (2005), no. 11, 1095–1101.
Search in Google Scholar Back to article
[8] LAKSHMANAN, M.—SENTHILKUMAR, D.V.: Dynamics of Nonlinear Time-Delay Systems. Springer-Verlag, Berlin, 2010.10.1007/978-3-642-14938-2
Search in Google Scholar Back to article
[9] DZHALLADOVA, I. A.—M. RŮŽIČKOVÁ, M.: Stability of the equilibrium of nonlinear dynamical systems, Tatra Mt. Math. Publ. 71 (2018), 71–80.
Search in Google Scholar Back to article
[10] SADANI, I.: On the stability of the functional equation f f(2x+y)+f(x+y2)=2f(x)f(y)f(x)+f(y)+2f(x+y)f(y−x)3f(y−x)−f(x+y)\[f(2x + y) + f(\frac{{x + y}}{2}) = \frac{{2f(x)f(y)}}{{f(x) + f(y)}} + \frac{{2f(x + y)f(y - x)}}{{3f(y - x) - f(x + y)}}\] Tatra Mt. Math. Publ 76 (2020), 71–80.
Back to article
[11] KHALOUTA, A.—KADE, A.: Solution of The fractional bratu-type equation via frac-tional residual power series method, Tatra Mt. Math. Publ. 76 (2020), no. 1, 127–142.
Search in Google Scholar Back to article
[12] DENG, W.—LI, C.—LU, J.: Stability analysis of linear fractional differential system with multiple time delays, Nonlinear Dyn. 48 (2007), no. 4, 409–416, doi: 10.1007/s11071-006-9094-0.10.1007/s11071-006-9094-0
Search in Google Scholar Back to article
[13] ČERMÁK, J.—DOŠLÁ, Z.—KISELA, T: Fractional differential equations with a constant delay: Stability and asymptotics of solutions, Appl. Math. Comput. 298 (2017), 336–350.
Search in Google Scholar Back to article
[14] SAWOOR, A. AL.: Stability analysis of fractional-order linear neutral delay differential–algebraic system described by the Caputo–Fabrizio derivative, Adv. Difference Equ. 2020, paper no. 531; (2020), https://doi.org/10.1186/s13662-020-02980-8.
Search in Google Scholar Back to article
[15] CHARTBUPAPAN, W.—BAGDASAR, O.—MUKDASAI, K.: A novel delay-dependent asymptotic stability conditions for differential and Riemann-Liouville fractional differential neutral systems with constant delays and nonlinear perturbation, Mathematics 8 (2020), no. 1, https://doi.org/10.3390/math8010082.10.3390/math8010082
Search in Google Scholar Back to article
[16] RADHA, M.—BALAMURALITHARAN, S.: A study on COVID-19 transmission dynamics: Stability analysis of SEIR model with Hopf bifurcation for effect of time delay, Adv. Differ. Equ. 2020Paper no.523 (2020), https://doi.org/10.1186/s13662-020-02958-6.10.1186/s13662-020-02958-6751346132989381
Search in Google Scholar Back to article
[17] PREETHILATHA, V.—RIHAN, F. A.—RAKKIYAPPAN, R.—VELMURUGAN, G.: A fractional order delay differential model for Ebola infection and CD8+ T cells response: Stability analysis and Hopf bifurcation, Int. J. Biomath. 10 (2017), no.8, https://doi.org/10.1142/S179352451750111X.10.1142/S179352451750111X
Search in Google Scholar Back to article
[18] Y. LI, Y.—WANG, Y.— LI, B.: Existence and finite-time stability of a unique almost periodic positive solution for fractional-order Lasota–Wazewska red blood cell models, Int. J. Biomath. 13, (2020), no.2, 16 pp, https://doi.org/10.1142/S1793524520500138.10.1142/S1793524520500138
Search in Google Scholar Back to article
[19] STAMOV, G.—STAMOVA, I.: Impulsive delayed Lasota–Wazewska fractional models: Global stability of integral manifolds, Mathematics 7 (2019), no. 11, 15 pp, https://doi.org/10.3390/math7111025.10.3390/math7111025
Search in Google Scholar Back to article
[20] BHALEKAR, S.—DAFTARDAR-GEJJI, V.: A predictor-corrector scheme for solving nonlinear delay differential equations of fractional order, J. Fractional Calculus and Appl. 1 (2011), no. 5, 1–9, http://www.fcaj.webs.com/.
Search in Google Scholar Back to article

Articles in this issue

DOI: https://doi.org/10.2478/tmmp-2021-0034 | Journal eISSN: 1338-9750 | Journal ISSN: 1210-3195

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Language: English

Page range: 135 - 144

Submitted on: Jan 5, 2021

Published on: Jan 1, 2022

Published by: Slovak Academy of Sciences, Mathematical Institute

In partnership with: Paradigm Publishing Services

Publication frequency: 1 issue per year

Keywords:

red blood cell,

stability,

time-delay,

fractional differential equation,

Caputo fractional derivative

Related subjects:

Mathematics,

General mathematics

© 2022 Santqshi Panigrahi, Sunita Chand, published by Slovak Academy of Sciences, Mathematical Institute
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Volume 80 (2021): Issue 3 (December 2021)