New qualitative results to delay integro-differential equations

[1] L.M. Berezanskii, Criteria for exponential stability of linear integro-differential equations, (Russian) Functionaldifferential equations (Russian), 66–69, Perm. Politekh. Inst., Perm, 1988.

[2] M. Bohner and O. Tunc, Qualitative analysis of integro-differential equations with variable retardation, Discrete Contin. Dyn. Syst. Ser. B 27 (2022), no. 2, 639.

[3] M. Bohner, O. Tun¸c and C. Tunc, Qualitative analysis of caputo fractional integro-differential equations with constant delays, Comp. Appl. ath. 40 (2021), 214.

[4] T.A. Burton, Volterra integral and differential equations, Second edition. Mathematics in Science and Engineering, 202. Elsevier B. V., Amsterdam, 2005.

[5] X. Chang and R. Wang, Stability of perturbed n -dimensional Volterra differential equations, Nonlinear Anal. 74 (2011), no. 5, 1672—1675.

[6] T.D. Chen and C.X. Ren, Asymptotic stability of integro-differential equations of convolution type, (Chinese) Acta Sci. Natur. Univ. Sunyatseni 41 (2002), no. 5, 22—24.

[7] A. Domoshnitsky and Y. Goltser, Floquet theorem and stability of linear integro-differential equations, Funct. Differ. Equ. 10 (2003), no. 3-4, 463—471.

[8] P. Eloe, M. Islam and B. Zhang, Uniform asymptotic stability in linear Volterra integro-differential equations with application to delay systems, Dynam. Syst. Appl. 9 (2000), no. 3, 331-–344.

[9] H. Engler, Asymptotic properties of solutions of nonlinear Volterra integro-differential equations, Results Math. 13 (1988), no. 1-2, 65-–80.

[10] M. Funakubo, T. Hara and S. Sakata, On the uniform asymptotic stability for a linear integro-differential equation of Volterra type, J. Math. Anal. Appl. 324 (2006), no. 2, 1036—1049.

[11] T. Furumochi and S. Matsuoka, Stability and boundedness in Volterra integro-differential equations, Mem. FacSci. Eng. Shimane Univ. Ser. B Math. Sci. 32 (1999), 25—40.

[12] S. Grace and E. Akin, Asymptotic behavior of certain integro-differential equations, Discrete Dyn. Nat. Soc. 2016 (2016), Art. ID 4231050, 6 pp.

[13] J.R. Graef and C. Tunc, Continuability and boundedness of multi-delay functional integro-differential equations of the second order, Rev. R. Acad. Cienc. Exactas F´ıs. Nat. Ser. A Math. RACSAM 109 (2015), no. 1, 169-–173.

[14] J. R. Graef, C. Tunc and H. S¸evli, Razumikhin qualitative analyses of Volterra integro-fractional delay differential equation with Caputo derivatives, Commun. Nonlinear Sci. Numer. Simul. 103 (2021), 106037.

[15] J.R Graef and O. Tunc, Asymptotic behavior of solutions of Volterra integro-differential equations with and without retardation, J. Integral Equ. Appl. 33 (2021), no. 3, 289–300.

[16] R. Grimmer and G. Seifert, Stability properties of Volterra integro-differential equations, J. Differ. Equ. 19 (1975), no. 1, 142-–166.

[17] S.I. Grossman and R.K. Miller, Perturbation theory for Volterra integro-differential systems, J. Differ. Equ. 8 (1970), 457-–474.

[18] J.K. Hale and S.M. Verduyn Lunel, Introduction to functional-differential equations, Applied Mathematical Sciences, 99. Springer-Verlag, New York, 1993.

[19] T. Hara, T. Yoneyama and T. Itoh, Asymptotic stability criteria for nonlinear Volterra integro-differential equations, Funkcial. Ekvac. 33 (1990), no. 1, 39—57.

[20] Y. Hino and S. Murakami, Stability properties of linear Volterra integro-differential equations in a Banach space, Funkcial. Ekvac. 48 (2005), no. 3, 367—392.

[21] C. Jin and J. Luo, Stability of an integro-differential equation, Comput. Math. Appl. 57 (2009), no. 7, 1080-–1088.

[22] V. Lakshmikantham and M. Rama Mohana Rao, Theory of integro-differential equations, Stability and Control: Theory, Methods and Applications, 1. Gordon and Breach Science Publishers, Lausanne, 1995.

[23] G.A. Leonov and V.B. Smirnova, Stability in the large of integro-differential equations of nondirect control systems, (Russian) Differentsial’nye Uravneniya 24 (1988), no. 3, 500–508, 549; translation in Differential Equations 24 (1988), no. 3, 359-–366.

[24] W.E. Mahfoud, Boundedness properties in Volterra integro-differential systems, Proc. Amer. Math. Soc. 100 (1987), no. 1, 37—45.

[25] C. Martinez, Bounded solutions of a forced nonlinear integro-differential equation, Dyn. Contin. Discrete Impuls. Syst. Ser. A Math. Anal. 9 (2002), no. 1, 35—42.

[26] R.K. Miller, Asymptotic stability properties of linear Volterra integro-differential equations, J. Differ. Equ. 10 (1971), 485-–506.

[27] S. Murakami, Exponential asymptotic stability for scalar linear Volterra equations, Differential Integral Equations 4 (1991), no. 3, 519—525.

[28] J.J. Nieto and O. Tun¸c, An application of Lyapunov–Razumikhin method to behaviors of Volterra integrodifferential equations, Rev. R. Acad. Cienc. Exactas F´ıs. Nat. (Esp.) 115 (2021), no. 4, 1–21.

[29] C. Pouchol and E. Trelat, Global stability with selection in integro-differential Lotka-Volterra systems modelling trait-structured populations, J. Biol. Dyn. 12 (2018), no. 1, 872—893.

[30] Y. Raffoul, Boundedness in nonlinear functional differential equations with applications to Volterra integrodifferential equations, J. Integral Equations Appl. 16 (2004), no. 4, 375—388.

[31] Y. Raffoul, Exponential stability and instability in finite delay nonlinear Volterra integro-differential equations, Dyn. Contin. Discrete Impuls. Syst. Ser. A Math. Anal. 20 (2013), no. 1, 95—106.

[32] M. Rama Mohana Rao and P. Srinivas, Asymptotic behavior of solutions of Volterra integro-differential equations, Proc. Amer. Math. Soc. 94 (1985), no. 1, 55—60.

[33] N. Sedova, On uniform asymptotic stability for nonlinear integro-differential equations of Volterra type, Cyber. Phys. 8 (2019), no. 3, 161—166.

[34] G. Seifert, Liapunov-Razumikhin conditions for asymptotic stability in functional differential equations of Volterra type, J. Differ. Equ. 16 (1974), 289—297.

[35] O.J. Staffans, A direct Lyapunov approach to Volterra integro-differential equations, SIAM J. Math. Anal. 19 (1988), no. 4, 879-–901.

[36] C. Tun¸c, Properties of solutions to Volterra integro-differential equations with delay, Appl. Math. Inf. Sci. 10 (2016), no. 5, 1775—1780.
[37] C. Tun¸c, Qualitative properties in nonlinear Volterra integro-differential equations with delay, J. Taibah Univ.
Sci. 11 (2017), no. 2, 309—314.
[38] C. Tun¸c, Asymptotic stability and boundedness criteria for nonlinear retarded Volterra integro-differential equations, J. King Saud Univ. Sci. 30 (2016), no. 4, 3531—3536.

[39] C. Tun¸c, Stability and boundedness in Volterra-integro differential equations with delays, Dynam. Syst. Appl. 26 (2017), no. 1, 121—130.

[40] C. Tun¸c, A remark on the qualitative conditions of nonlinear IDEs, Int. J. Math. Comput. Sci. 15 (2020), no. 3, 905—922.

[41] C. Tun¸c and O. Tun¸c, On behaviors of functional Volterra integro-differential equations with multiple time-lags, J. Taibah Univ. Sci. 12 (2018), no. 2, 173—179.

[42] C. Tun¸c and O. Tun¸c, New qualitative criteria for solutions of Volterra integro-differential equations, Arab J. Basic Appl. Sci. 25 (2018), no. 3, 158-165.

[43] C. Tun¸c and O. Tun¸c, New results on the stability, integrability and boundedness in Volterra integro-differential equations, Bull. Comput. Appl. Math. 6 (2018), no. 1, 41–58.

[44] C. Tun¸c and O. Tun¸c, A note on the qualitative analysis of Volterra integro-differential equations, J. Taibah Univ. Sci. 13 (2019), no. 1, 490-–496.

[45] O. Tunc, C. Tunc and Y. Wang, Delay-dependent stability, integrability and boundedeness criteria for delay differential systems, Axioms 10 (2021), no. 3, 138.

[46] O. Tun¸c, O. Atan, C. Tun¸c and J. C. Yao, ¨ Qualitative analyses of integro-fractional differential equations with Caputo derivatives and retardations via the Lyapunov–Razumikhin method, Axioms 10 (2021), no. 2, 58.

[47] C. Tun¸c and O. Tun¸c, On the stability, integrability and boundedness analyses of systems of integro-differential equations with time-delay retardation, RACSAM 115 (2021), 115.

[48] C. Tun¸c, O. Tun¸c, Y. Wang and J.C. Yao, Qualitative analyses of differential systems with time-varying delays via Lyapunov-Krasovskiˇı approach, Math. 9 (2021), no. 11, 1196.

[49] C. Tun¸c, Y. Wang, O. Tun¸c and J.C. Yao, New and improved criteria on fundamental properties of solutions of integro—delay differential equations with constant delay, Math. 9 (2021), no. 24, 3317.

[50] O. Tun¸c, On the behaviors of solutions of systems of non-linear differential equations with multiple constant delays, RACSAM 115 (2021), 164.

[51] O. Tun¸c, On the qualitative analyses of integro-differential equations with constant time lag, Appl. Math. Inf. Sci. 14 (2020), no. 1, 57—63.

[52] J. Vanualailai and S. Nakagiri, Stability of a system of Volterra integro-differential equations, J. Math. Anal. Appl. 281 (2003), no. 2, 602-–619.

[53] K. Wang, Uniform asymptotic stability in functional-differential equations with infinite delay, Ann. Differ. Equ. 9 (1993), no. 3, 325—335.

[54] Q. Wang, The stability of a class of functional differential equations with infinite delays, Ann. Differ. Equ. 16 (2000), no. 1, 89-–97.

[55] A.M. Wazwaz, Linear and nonlinear integral equations: Methods and applications, Higher Education Press, Beijing; Springer, Heidelberg, 2011.

[56] Z.C. Wang, Z.X. Li and J.H. Wu, Stability properties of solutions of linear Volterra integro-differential equations,Tohoku Math. J. 37 (1985), no. 4, 455—462.

[57] B. Zhang, Necessary and sufficient conditions for stability in Volterra equations of non-convolution type, Dynam. Systems Appl. 14 (2005), no. 3-4, 525-–549.

[58] B. Zhou and A.V. Egorov, Razumikhin and Krasovskiı stability theorems for time-varying time-delay systems, Automatica J. IFAC 71 (2016), 281–291.

[59] Z.D. Zhang, Asymptotic stability of Volterra integro-differential equations, J. Harbin Inst. Tech. 1990 (1990), no. 4, 11-–19.

[60] X. Xu, L. Liu and G. Feng, Stability and stabilization of infinite delay systems: a Lyapunov-based approach, IEEE Trans. Automat. Control 65 (2020), no. 11, 4509-–4524.