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Stability in first order delay integro-differential equations

Year 2020, Volume: 22 Issue: 2, 660 - 668, 10.04.2020
https://doi.org/10.25092/baunfbed.744661

Abstract

In this study, some results are given concerning the behavior of the solutions for linear delay integro-differential equations. These results are obtained by the use of two distinct real roots of the corresponding characteristic equation.

References

  • Appleby, J.A.D. and Reynolds, D.W., On the non-exponential convergence of asymptotically stable solutions of linear scalar Volterra integro – differential equations, Journal of Integral Equations and Applications, 14, 2, (2002).
  • Funakubo, M., Hara, T. and Sakata, S., On the uniform asymptotic stability for a linear integro-differential equation of Volterra type, Journal of Mathematical Analysis and Applications, 324, 1036–1049, (2006).
  • Gopalsamy, K., Stability and decay rates in a class of linear integro-differential systems, Funkcialaj Ekvacioj, 26, 251-261, (1983).
  • Kordonis, I.-G.E. and Philos, Ch.G., The behavior of solutions of linear integro- differential equations with unbounded delay, Computers & Mathematics with Applications, 38, 45-50, (1999).
  • Koto, T., Stability of Runge - Kutta methods for delay integro – differential equations, Journal of Computational and Applied Mathematics, 145, 483-492, (2002).
  • Volterra, V., Sur la théorie mathématique des phénoménes héréditaires, Journal de Mathématiques Pures et Appliquées, 7(9), 249-298, (1928).
  • Philos, Ch.G. and Purnaras, I.K., Asymptoti properties, nonoscillation, and stability for scalar first order linear autonomous neutral delay differential equations, Electronic Journal of Differential Equations, 2004, 03, 1-17, (2004).
  • Philos, Ch. G. and Purnaras, I. K., A result on the behavior of the solutions for scalar first order linear autonomous neutral delay differential equations, Mathematical Proceedings of the Cambridge Philosophical Society, 140, 349-358, (2006).
  • Philos, Ch.G. and Purnaras, I.K., On the behavior of the solutions for certainfirst order linear autonomous functional differential equations, Rocky Mountain Journal of Mathematics, 36, 1999-2019, (2006).
  • Hale, J.K. and Verduyn Lunel, S.M., Introduction to Functional Differential Equations, Springer, Berlin, Heidelberg, New York, (1993).
  • Kolmanovski, V. and Myshkis, A., Applied Theory of Functional Differential Equations, Kluver Academic, Dordrecht, (1992).
  • Kuang, Y., Delay Differential Equations with Applications in Population Dynamics, Academic Press, San Diego, (1993).
  • Burton, T.A., Volterra Integral and Differential Equations, Academic Press, New York, (1983).
  • Corduneanu, C., Integral Equations and Applications, Cambridge University Press, New York, (1991).
  • Yeniçerioğlu, A.F. and Yalçınbaş S., On the stability of delay integro-differential equations, Mathematical and Computational Applications, 12(1), 51-58, (2007).

Birinci mertebeden gecikmeli integro-diferansiyel denklemlerde kararlılık

Year 2020, Volume: 22 Issue: 2, 660 - 668, 10.04.2020
https://doi.org/10.25092/baunfbed.744661

Abstract

Bu çalışmada, doğrusal gecikmeli integro-diferansiyel denklemler için çözümlerin davranışı ile ilgili bazı sonuçlar verilmiştir. Bu sonuçlar, karşılık gelen karakteristik denklemin iki ayrı reel kökünün kullanılmasıyla elde edilmiştir.

References

  • Appleby, J.A.D. and Reynolds, D.W., On the non-exponential convergence of asymptotically stable solutions of linear scalar Volterra integro – differential equations, Journal of Integral Equations and Applications, 14, 2, (2002).
  • Funakubo, M., Hara, T. and Sakata, S., On the uniform asymptotic stability for a linear integro-differential equation of Volterra type, Journal of Mathematical Analysis and Applications, 324, 1036–1049, (2006).
  • Gopalsamy, K., Stability and decay rates in a class of linear integro-differential systems, Funkcialaj Ekvacioj, 26, 251-261, (1983).
  • Kordonis, I.-G.E. and Philos, Ch.G., The behavior of solutions of linear integro- differential equations with unbounded delay, Computers & Mathematics with Applications, 38, 45-50, (1999).
  • Koto, T., Stability of Runge - Kutta methods for delay integro – differential equations, Journal of Computational and Applied Mathematics, 145, 483-492, (2002).
  • Volterra, V., Sur la théorie mathématique des phénoménes héréditaires, Journal de Mathématiques Pures et Appliquées, 7(9), 249-298, (1928).
  • Philos, Ch.G. and Purnaras, I.K., Asymptoti properties, nonoscillation, and stability for scalar first order linear autonomous neutral delay differential equations, Electronic Journal of Differential Equations, 2004, 03, 1-17, (2004).
  • Philos, Ch. G. and Purnaras, I. K., A result on the behavior of the solutions for scalar first order linear autonomous neutral delay differential equations, Mathematical Proceedings of the Cambridge Philosophical Society, 140, 349-358, (2006).
  • Philos, Ch.G. and Purnaras, I.K., On the behavior of the solutions for certainfirst order linear autonomous functional differential equations, Rocky Mountain Journal of Mathematics, 36, 1999-2019, (2006).
  • Hale, J.K. and Verduyn Lunel, S.M., Introduction to Functional Differential Equations, Springer, Berlin, Heidelberg, New York, (1993).
  • Kolmanovski, V. and Myshkis, A., Applied Theory of Functional Differential Equations, Kluver Academic, Dordrecht, (1992).
  • Kuang, Y., Delay Differential Equations with Applications in Population Dynamics, Academic Press, San Diego, (1993).
  • Burton, T.A., Volterra Integral and Differential Equations, Academic Press, New York, (1983).
  • Corduneanu, C., Integral Equations and Applications, Cambridge University Press, New York, (1991).
  • Yeniçerioğlu, A.F. and Yalçınbaş S., On the stability of delay integro-differential equations, Mathematical and Computational Applications, 12(1), 51-58, (2007).
There are 15 citations in total.

Details

Primary Language English
Journal Section Research Articles
Authors

Ali Fuat Yeniçerioğlu 0000-0002-1063-0538

Cüneyt Yazıcı This is me 0000-0002-4535-510X

Publication Date April 10, 2020
Submission Date January 15, 2020
Published in Issue Year 2020 Volume: 22 Issue: 2

Cite

APA Yeniçerioğlu, A. F., & Yazıcı, C. (2020). Stability in first order delay integro-differential equations. Balıkesir Üniversitesi Fen Bilimleri Enstitüsü Dergisi, 22(2), 660-668. https://doi.org/10.25092/baunfbed.744661
AMA Yeniçerioğlu AF, Yazıcı C. Stability in first order delay integro-differential equations. BAUN Fen. Bil. Enst. Dergisi. April 2020;22(2):660-668. doi:10.25092/baunfbed.744661
Chicago Yeniçerioğlu, Ali Fuat, and Cüneyt Yazıcı. “Stability in First Order Delay Integro-Differential Equations”. Balıkesir Üniversitesi Fen Bilimleri Enstitüsü Dergisi 22, no. 2 (April 2020): 660-68. https://doi.org/10.25092/baunfbed.744661.
EndNote Yeniçerioğlu AF, Yazıcı C (April 1, 2020) Stability in first order delay integro-differential equations. Balıkesir Üniversitesi Fen Bilimleri Enstitüsü Dergisi 22 2 660–668.
IEEE A. F. Yeniçerioğlu and C. Yazıcı, “Stability in first order delay integro-differential equations”, BAUN Fen. Bil. Enst. Dergisi, vol. 22, no. 2, pp. 660–668, 2020, doi: 10.25092/baunfbed.744661.
ISNAD Yeniçerioğlu, Ali Fuat - Yazıcı, Cüneyt. “Stability in First Order Delay Integro-Differential Equations”. Balıkesir Üniversitesi Fen Bilimleri Enstitüsü Dergisi 22/2 (April 2020), 660-668. https://doi.org/10.25092/baunfbed.744661.
JAMA Yeniçerioğlu AF, Yazıcı C. Stability in first order delay integro-differential equations. BAUN Fen. Bil. Enst. Dergisi. 2020;22:660–668.
MLA Yeniçerioğlu, Ali Fuat and Cüneyt Yazıcı. “Stability in First Order Delay Integro-Differential Equations”. Balıkesir Üniversitesi Fen Bilimleri Enstitüsü Dergisi, vol. 22, no. 2, 2020, pp. 660-8, doi:10.25092/baunfbed.744661.
Vancouver Yeniçerioğlu AF, Yazıcı C. Stability in first order delay integro-differential equations. BAUN Fen. Bil. Enst. Dergisi. 2020;22(2):660-8.