Stability in first order delay integro-differential equations
Yıl 2020,
Cilt: 22 Sayı: 2, 660 - 668, 10.04.2020
Ali Fuat Yeniçerioğlu
,
Cüneyt Yazıcı
Öz
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.
Kaynakça
- 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
Yıl 2020,
Cilt: 22 Sayı: 2, 660 - 668, 10.04.2020
Ali Fuat Yeniçerioğlu
,
Cüneyt Yazıcı
Öz
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.
Kaynakça
- 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).