164
Views
9
CrossRef citations to date
0
Altmetric
Articles

Random differential equations with discrete delay

, &
Pages 699-707 | Received 02 Feb 2019, Accepted 15 Apr 2019, Published online: 29 Apr 2019

References

  • Erneux, T. (2009). Applied Delay Differential Equations. New York, NY: Springer.
  • Kuang, Y. (1993). Delay Differential Equations with Applications in Population Dynamics. San Diego, CA: Academic Press.
  • Kolmanovskii, V. B., Shaikhet, L. (1997). Control of Systems with Aftereffect. New York, NY: AMS, Translations of Mathematical Monographs.
  • Fridman, E., Shaikhet, L. (2017). Stabilization by using artificial delays: An LMI approach. Automatica 81:429–437. DOI:10.1016/j.automatica.2017.04.015.
  • Shaikhet, L., Korobeinikov, A. (2016). Stability of a stochastic model for HIV-1 dynamics within a host. Appl. Anal. 95(6):1228–1238. DOI:10.1080/00036811.2015.1058363.
  • Caraballo, T., Colucci, R., Guerrini, L. (2018). On a predator prey model with nonlinear harvesting and distributed delay. Commun. Pure Appl. Anal. 17(6):2703–2727. DOI:10.3934/cpaa.2018128.
  • Caraballo, T., Garrido-Atienza, M. J., Schmalfuss, B., Valero, J. (2017). Attractors for a random evolution equation with infinite memory: Theoretical results. Discrete Cont. Dyn.-B 22(5):1779–1800. DOI:10.3934/dcdsb.2017106.
  • Krapivsky, P. L., Luck, J. M., Mallick, K. (2011). On stochastic differential equations with random delay. J. Stat. Mech. DOI:10.1088/1742-5468/2011/10/P10008.
  • Liu, S., Debbouche, A., Wang, J. R. (2017). On the iterative learning control for stochastic impulsive differential equations with randomly varying trial lengths. J. Comput. Appl. Math. 312:47–57. DOI:10.1016/j.cam.2015.10.028.
  • Soong, T. T. (1973). Random Differential Equations in Science and Engineering. New York, NY: Academic Press.
  • Dorini, F. A., Cecconello, M. S., Dorini, L. B. (2016). On the logistic equation subject to uncertainties in the environmental carrying capacity and initial population density. Commun. Nonlinear Sci. 33:160–173. DOI:10.1016/j.cnsns.2015.09.009.
  • Slama, H., El-Bedwhey, N. A., El-Depsy, A., Selim, M. M. (2017). Solution of the finite Milne problem in stochastic media with RVT technique. Eur. Phys. J. Plus 132(12):505. DOI:10.1140/epjp/i2017-11763-6.
  • Nouri, K., Ranjbar, H., Torkzadeh, L. (2019). Modified stochastic theta methods by ODEs solvers for stochastic differential equations. Commun. Nonlinear Sci. 68:336–346. DOI:10.1016/j.cnsns.2018.08.013.
  • Lupulescu, V., Ntouyas, K. N. (2012). Random fractional differential equations. Int. Electron. J. Pure Appl. Math. 4(2):119–136.
  • Lupulescu, V., O'Regan, D., Ur Rahman, G. (2014). Existence results for random fractional differential equations. Opmath. 34(4):813–825. DOI:10.7494/OpMath.2014.34.4.813.
  • Loève, M. (1977). Probability Theory, Vol. 2. New York, NY: Springer.
  • Strand, J. L. (1970). Random ordinary differential equations. J. Differ. Equ. 7(3):538–553. DOI:10.1016/0022-0396(70)90100-2.
  • Villafuerte, L., Braumann, C. A., Cortés, J. C., Jódar, L. (2010). Random differential operational calculus: Theory and applications. Comput. Math. Appl. 59(1):115–125. DOI:10.1016/j.camwa.2009.08.061.
  • Granas, A., Dugundji, J. (2003). Fixed Point Theory. New York, NY: Springer-Verlag.
  • Khusainov, D. Y., Pokojovy, M., Azizbayov, E. (2014). Classical solvability for linear 1D heat equation with constant delay. Zhurnal Obchyslyuval’nï ta Prykladnoï Matematyky 115:76–87.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.