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This work aims to investigate a delay hematopoiesis model where the delay depends on both the time and the current density of mature blood cells. Based on the Banach contraction principle, the Schauder's fixed point theorem and some properties of a Green's function, we establish several interesting existence and uniqueness results of positive periodic solutions for the proposed model. The derived results are new and generalize some previous studies.
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V. Berinde, Existence and approximation of solutions of some first order iterative differential equations, Miskolc Math. 11(1) (2010), 13–26.
A. Bouakkaz, A. Ardjouni and A. Djoudi, Periodic solutions for a second order nonlinear functional differential equation with iterative terms by Schauder fixed point theorem, Acta Math. Univ. Comen. 87(2) (2018), 223–235.
A. Bouakkaz, A. Ardjouni, R. Khemis and A. Djoudi, Periodic solutions of a class of third order functional differential equations with iterative source terms, Bol. Soc. Mat. Mex. 26(2) (2020), 443–458.
A. Bouakkaz, Bounded solutions to a three-point fourth-order iterative boundary value problem, Rocky Mountain J. Math. 52(3) (2022), 793–803.
A. Bouakkaz, Positive periodic solutions for a class of first-order iterative differential equations with an application to a Hematopoiesis model, Carpathian J. Math. 38(2) (2022), 347–355.
A. Bouakkaz and R. Khemis, Positive periodic solutions for a class of second-order differential equations with state-dependent delays, Turkish J. Math. 44(4) (2020), 1412–1426.
A. Bouakkaz and R. Khemis, Positive periodic solutions for revisited Nicholson’s blowflies equation with iterative harvesting term, J. Math. Anal. Appl. 494(2) (2021), 124663.
S. Cheraiet, A. Bouakkaz and R. Khemis, Bounded positive solutions of an iterative three point boundary-value problem with integral boundary conditions, J. Appl. Math. Comput. 65(1) (2020), 597–610.
S. Chouaf, A. Bouakkaz and R. Khemis, On bounded solutions of a second-order iterative boundary value problem, Turkish J. Math. 46(SI-1) (2022), 453–464.
S. Chouaf, R. Khemis and A. Bouakkaz, Some existence results on positive solutions for an iterative second-order boundary-value problem with integral boundary conditions, Bol. Soc. Parana. Mat. (3) 4 (2022), 01–10.
E-R. Kaufmann, Existence and uniqueness of solutions for a second-order iterative boundary value problem functional differential equation, Electron. J. Differ. Equ. 2018:150 (2018) (2018), 1-6.
R. Khemis, A. Ardjouni, A. Bouakkaz and A. Djoudi, Periodic solutions of a class of third order differential equations with two delays depending on time and state, Comment. Math. Univ. Carolin. 60(3) (2019), 379–399.
M. C. Mackey and L. Glass, Oscillation and chaos in physiological control systems, Science. 197(4300) (1977), 287–289.
E. Schröder, Über iterate funktionen, Math. Ann. 3 (1871), 295–322.
D. Yang and W. Zhang, Solutions of equivariance for iterative differential equations, Appl. Math. Lett. 17(7) (2004), 759–765.
H-Y. Zhao and M. FeˇCkan, Periodic solutions for a class of differential equations with delays depending on state, Math. Commun. 23(7) (2018), 29–42.
H-Y. Zhao andJ. Liu, Periodic solutions of an iterative functional differential equation with variable coefficients, Math. Meth. Appl. 40 (2011), 286–292.