Further results on Ulam stability for a system of first-order nonsingular delay differential equations

• Autorzy: Zada Akbar , Pervaiz Bakhtawar , Alzabut Jehad , Shah Syed Omar

Identyfikatory

DOI

10.1515/dema-2020-0018

• Języki publikacji: EN

Abstrakty

EN

This paper is concerned with a system governed by nonsingular delay differential equations. We study the β-Ulam-type stability of the mentioned system. The investigations are carried out over compact and unbounded intervals. Before proceeding to the main results, we convert the system into an equivalent integral equation and then establish an existence theorem for the addressed system. To justify the application of the reported results, an example along with graphical representation is illustrated at the end of the paper.

Słowa kluczowe

EN

delayed exponential matrix; delay differential system; representation of solutions; β-Hyers-Ulam-Rassias stability

PL

macierz wykładnicza; stabilność Hyersa-Ulama-Rassiasa

• Wydawca: De Gruyter
• Czasopismo: Demonstratio Mathematica
• Rocznik: 2020
• Tom: Vol. 53, nr 1
• Strony: 225--235
• Opis fizyczny: Bibliogr. 17 poz., rys.

Twórcy

autor

Zada Akbar

• Department of Mathematics, University of Peshawar, Peshawar, 25000, Pakistan

autor

Pervaiz Bakhtawar

• Department of Mathematics, University of Peshawar, Peshawar, 25000, Pakistan

autor

Alzabut Jehad

• Department of Mathematics and General Sciences, Prince Sultan University, 11586, Riyadh, Saudi Arabia

autor

Shah Syed Omar

• Department of Mathematics, University of Peshawar, Peshawar, 25000, Pakistan; Department of Physical and Numerical Sciences, Qurtuba University of Science and Information Technology Peshawar, Dera Ismail Khan, Pakistan

Bibliografia

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• [3] Z. You, J. R. Wang, and D. O’Regan, Exponential stability and relative controllability of nonsingular delay systems, Bull. Braz. Math. Soc. (N.S.) 50(2019), 457-479, DOI: 10.1007/s00574-018-0110-z.
• [4] S. M. Ulam, Problems in Modern Mathematics, Rend. Chap. VI, Wiley, New York, 1960.
• [5] D. H. Hyers, On the stability of the linear functional equation, Proc. Natl. Acad. Sci. USA 27(1941), no. 4, 222-224, DOI: 10.1073/pnas.27.4.222.
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• [13] G. M. Selvam, D. Baleanu, J. Alzabut, D. Vignesh, and S. Abbas, On Hyers-Ulam Mittag-Leffler stability of discrete fractional Duffing equation with application on inverted pendulum, Adv. Difference Equ. 2020(2020), 456, DOI: 10.1186/s13662-020-02920-6.
• [14] W. Sudsutad, J. Alzabut, S. Nontasawatsri, and C. Thaiprayoon, Stability analysis for a generalized proportional fractional Langevin equation with variable coefficient and mixed integro-differential boundary conditions, J. Nonlinear Funct. Anal. 2020(2020), 23, DOI: 10.23952/jnfa.2020.23.
• [15] X. Wang, M. Arif, and A. Zada, β-Hyers-Ulam-Rassias stability of semilinear nonautonomous impulsive system, Symmetry 11(2019), 231, DOI: 10.3390/sym11020231.
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Uwagi

PL

Opracowanie rekordu ze środków MNiSW, umowa Nr 461252 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2020).