Existence uniqueness and stability for certain operators of nonlinear system of differential equations

Authors

  • Dawoud .S Abdullah University of Zakho
  • Ava Rafeeq University of Zakho
  • Raad N. Butris University of Zakho

DOI:

https://doi.org/10.31763/businta.v7i2.656

Keywords:

Operatot nonlinear, Equations, Differential

Abstract

This research contributes to the understanding of nonlinear systems of differential equations with operators, specifically in the context of generalizing Volterra and Fredholm integral equations. The use of the Picard approximation method, Banach fixed point theorem, and stability analysis further enhances the analysis of the solutions. The examples provided help to solidify the theoretical findings and highlight their applicability.

References

L. Wei, R. P. Agarwal, and P. J. Y. Wong, “Discussion on the existence and uniqueness of solution to nonlinear integro-differential systems,” Comput. Math. with Appl., vol. 69, no. 5, pp. 374–389, Mar. 2015, doi: 10.1016/j.camwa.2014.12.007.

A. Ashyralyev and Y. A. Sharifov, “Existence and Uniqueness of Solutions for the System of Nonlinear Fractional Differential Equations with Nonlocal and Integral Boundary Conditions,” Abstr. Appl. Anal., vol. 2012, pp. 1–14, 2012, doi: 10.1155/2012/594802.

H. Brunner, “Numerical Analysis and Computational Solution of Integro-Differential Equations,” in Contemporary Computational Mathematics - A Celebration of the 80th Birthday of Ian Sloan, Cham: Springer International Publishing, 2018, pp. 205–231, doi: 10.1007/978-3-319-72456-0_11.

M. Muslim, A. Kumar, and M. Fečkan, “Existence, uniqueness and stability of solutions to second order nonlinear differential equations with non-instantaneous impulses,” J. King Saud Univ. - Sci., vol. 30, no. 2, pp. 204–213, Apr. 2018, doi: 10.1016/j.jksus.2016.11.005.

A. Devi, A. Kumar, D. Baleanu, and A. Khan, “On stability analysis and existence of positive solutions for a general non-linear fractional differential equations,” Adv. Differ. Equations, vol. 2020, no. 1, p. 300, Dec. 2020, doi: 10.1186/s13662-020-02729-3.

R. N. Butris and A. S. Rafeeq, “Existence and uniqueness solution of a boundary value problems for integro-differential equation with parameter,” Ital. J. Pure Appl. Math., vol. 2017, no. 37, pp. 431–440, 2017, [Online]. Available at: https://ijpam.uniud.it/online_issue/201737/39-ButrisRafeeq.pdf.

R. Bellman, “Existence and Uniqueness Theorems,” in Dynamic Programming, Princeton University Press, 2021, pp. 116–151, doi: 10.2307/j.ctv1nxcw0f.8.

A. M. Malbanji, “Solving Fourth Order Differential Non-Linear Equations, Existence and Uniqueness,” p. 45, 2017. [Online]. Available at : https://dspace.aus.edu/xmlui/bitstream/handle/11073/8860/29.232-2017.08 Amer Mahmoud Malbanji.pdf?sequence=1&isAllowed=y.

Z. Eidinejad, R. Saadati, and M. De La Sen, “Picard Method for Existence, Uniqueness, and Gauss Hypergeomatric Stability of the Fractional-Order Differential Equations,” Math. Probl. Eng., vol. 2021, pp. 1–9, Jul. 2021, doi: 10.1155/2021/7074694.

A. Sh, “Periodic Solutions For Some Classes Of Non-Linear Systems Of Integro-Differential Equations,” 2020.

F. Battelli, M. Feckan, and M. Franca, “On the chaotic behavior of a compressed beam,” Dyn. Partial Differ. Equations, vol. 4, no. 1, pp. 55–86, 2007, doi: 10.4310/DPDE.2007.v4.n1.a2.

R. Butris, “Existence of a periodic solutions for certain system of nonlinear integro-differential equations,” J. Educ. Sci., vol. 21, no. 2, pp. 103–117, Jun. 2008, doi: 10.33899/edusj.2008.51249.

D. N. Chate and S. Mahavidyalaya, “Study Of Iterative Methods In Fixed Point Theory With Applications,” pp. 1-11, 2020. [Online]. Available at: https://shodhgangotri.inflibnet.ac.in/bitstream/20.500.14146/9107/1/01_synopsis.pdf.

R. Shukla, R. Pant, and W. Sinkala, “A General Picard-Mann Iterative Method for Approximating Fixed Points of Nonexpansive Mappings with Applications,” Symmetry (Basel)., vol. 14, no. 8, p. 1741, Aug. 2022, doi: 10.3390/sym14081741.

V. Pata, “Fixed-point theorems and applications,” in Functional Analysis with Applications,” vol. 116, De Gruyter, 2019, pp. 309–374, doi: 10.1515/9783110657722-010.

H. K. Pathak, “An Introduction to Nonlinear Analysis and Fixed Point Theory,” Singapore: Springer Singapore, p. 830, 2018, doi: 10.1007/978-981-10-8866-7.

A. M. Samoilenko and N. A. Perestyuk, “Impulsive Differential Equations, vol. 14. World Scientific, p. 472, 1995, doi: 10.1142/2892.

S. A. Kolesnik and N. A. Bulychev, “Numerical analytic method for solving the inverse coefficient problem of heat conduction in anisotropic half-space,” J. Phys. Conf. Ser., vol. 1474, no. 1, p. 012024, Feb. 2020, doi: 10.1088/1742-6596/1474/1/012024.

S. Mungkasi and D. Widjaja, “A numerical-analytical iterative method for solving an electrical oscillator equation,” TELKOMNIKA (Telecommunication Comput. Electron. Control., vol. 19, no. 4, p. 1218, Aug. 2021, doi: 10.12928/telkomnika.v19i4.18987.

A. M. Samoilenko, “Averaging method for investigating systems subjected to an impulsive action,” Ukr. Math. J., vol. 19, no. 5, pp. 586–593, Sep. 1969, doi: 10.1007/BF01085298

Downloads

Published

2023-12-05

How to Cite

Abdullah , D. .S, Rafeeq, A., & Butris , R. N. (2023). Existence uniqueness and stability for certain operators of nonlinear system of differential equations. Bulletin of Social Informatics Theory and Application, 7(2), 193–204. https://doi.org/10.31763/businta.v7i2.656

Issue

Section

Articles