A note on the qualitative analysis of Volterra integro-differential equations

References

• Burton TA. Volterra integral and differential equations. 2nd ed. Mathematics in Science and Engineering. Amsterdam: Elsevier BV; 2005; p. 202.
   Google Scholar
• Rahman M. Integral equations and their applications. Southampton: WIT Press; 2007.
   Google Scholar
• Samoilenko AM, Perestyuk NA. Impulsive differential equations. With a preface by Yu. A. Mitropol’skii and a supplement by S. I. Trofimchuk. Translated from the Russian by Y. Chapovsky. World Scientific Series on Nonlinear Science. Series A: Monographs and Treatises, NJ: 14. River Edge: World Scientific; 1995.
   Google Scholar
• Wazwaz AM. Linear and nonlinear integral equations. Methods and applications. Beijing: Higher Education Press; 2011.
   Google Scholar
• Alahmadi F, Raffoul Y, Alharbi S. Boundedness and stability of solutions of nonlinear Volterra integro-differential equations. Adv Dyn Syst Appl. 2018;13(1):19–31.
   Google Scholar
• Becker LC. Uniformly continuous solutions of Volterra equations and global asymptotic stability. Cubo. 2009;11(3):1–24.
   Google Scholar
• El Hajji M. Boundedness and asymptotic stability of nonlinear Volterra integro-differential equations using Lyapunov functional. J King Saud Univ Sci. 2018; in press.
   Google Scholar
• Graef JR, Tunç C, Şevgin S. Behavior of solutions of non-linear functional Voltera integro-differential equations with multiple delays. Dyn Syst Appl. 2016;25(1–2):39–46.
   Web of Science ®Google Scholar
• Lakshmikantham V, Bainov DD, Simeonov PS. Theory of impulsive differential equations. Series in modern applied mathematics, 6. Teaneck (NJ): World Scientific; 1989.
   Google Scholar
• Raffoul Y, Rai H. Uniform stability in nonlinear infinite delay Volterra integro-differential equations using Lyapunov functionals. Nonauton. Dyn Syst. 2016;3:14–23.
   Google Scholar
• Rama Mohana Rao M, Srinivas P. Asymptotic behavior of solutions of Volterra integro-differential equations. Proc Am Math Soc. 1985;94(1):55–60.
   Web of Science ®Google Scholar
• Tunç C. A note on the qualitative behaviors of non-linear Volterra integro-differential equation. J Egyptian Math Soc. 2016;24(2):187–192.
   Google Scholar
• Tunç C. New stability and boundedness results to Volterra integro-differential equations with delay. J Egyptian Math Soc. 2016;24(2):210–213.
   Google Scholar
• Tunç C. Properties of solutions to Volterra integro-differential equations with delay. Appl Math Inf Sci. 2016;10(5):1775–1780.
   Google Scholar
• Tunç C. Qualitative properties in nonlinear Volterra integro-differential equations with delay. J Taibah Univ Sci. 2017;11(2):309–314.
   Web of Science ®Google Scholar
• Tunç C. Asymptotic stability and boundedness criteria for nonlinear retarded Volterra integro-differential equations. J King Saud Univ Sci. 2016;30(4):3531–3536.
   Web of Science ®Google Scholar
• Tunc C. Stability and boundedness in Volterra-integro differential equations with delays. Dyn Syst Appl. 2017;26(1):121–130.
   Web of Science ®Google Scholar
• Tunç C, Mohammed SA. A remark on the stability and boundedness criteria in retarded Volterra integro-differential equations. J Egyptian Math Soc. 2017;25(4):363–368.
   Google Scholar
• Tunç C, Mohammed SA. On the stability and uniform stability of retarded integro-differential equations. Alexandria Eng J. 2018;57:3501–3507.
   Web of Science ®Google Scholar
• Tunç C, Tunç O. On the exponential study of solutions of Volterra integro-differential equations with time lag. Electron J Math Anal Appl. 2018;6(1):253–265.
   Google Scholar
• Tunç C, Tunç O. New results on the stability, integrability and boundedness in Volterra integro-differential equations. Bull. Comput Appl Math. 2018;6(1):41–58.
   Web of Science ®Google Scholar
• Tunç C, Tunç O. New results on behaviors of functional Voltera integro-differential equations with multiple time-lags. Jordan J Math Stat. 2018;11(2):107–124.
   Web of Science ®Google Scholar
• Tunç C, Tunç O. New qualitative criteria for solutions of Volterra integro-differential equations. Arab J Basic Appl Sci. 2018;25(3):158–165.
   Google Scholar
• Wang K. Uniform asymptotic stability in functional-differential equations with infinite delay. Ann Diff Equ. 1993;9(3):325–335.
   Google Scholar
• Wang Q. The stability of a class of functional differential equations with infinite delays. Ann. Diff Equ. 2000;16(1):89–97.
   Google Scholar