Exponential Stability of Integro-Differential Volterra Equation on Time Scales

[1] ADIVAR, M.—RAFFOUL, Y. N.: Existence of resolvent for Volterra integral equations on time scales, Bull. Austral. Math. Soc. 82 (2010), no. 1, 139–155. Search in Google Scholar

[2] AKIN-BOHNER, E.—BOHNER, M.—AKIN, F.: Pachpatte inequalities on time scales, J. Inequal. Pure Appl. Math. 6 (2005), no. 1, Article 6. Search in Google Scholar

[3] BEREZANSKY, L.—MIGDA, M.—SCHMEIDEL, E.: Some stability conditions for scalar Volterra difference equations, Opuscula Math. 36 (2016), no. 4, 459–470. Search in Google Scholar

[4] BOHNER, M.—PETERSON, A.: Dynamic Equations On Time Scales. Birkhäuser, Basel, 2001. Search in Google Scholar

[5] BOHNER, M.—PETERSON, A.: Advances in Dynamic Equations on Time Scales. Birkhäuser, Boston, Ma, 2003. Search in Google Scholar

[6] DIBLÍK, J.—RŮŽIČKOVÁ, M.—SCHMEIDEL, E.: Asymptotically periodic solutions of Volterra difference equations, Tatra Mt. Math. Publ. 43 (2009), 51–61. Search in Google Scholar

[7] DU, N. H.—TIEN, L. H.: On the exponential stability of dynamic equations on time scales, J. Math. Anal. Appl. 331 (2007), 1159–1174. Search in Google Scholar

[8] GIREJKO, E., MACHADO, L.—MALINOWSKA, A. B.—MARTINS, N.: Krause’s model of opinion dynamics on isolated time scales, Math. Methods Appl. Sci. 39 (2016), no. 18, 5302–5314. Search in Google Scholar

[9] GIREJKO, E.—MACHADO, L.—MALINOWSKA, A. B.—MARTINS, N.: On consensus in the Cucker-Smaletype model on isolated time scale, Discrete Contin. Dyn. Syst. 11 (2018), no. 1, 77–89. Search in Google Scholar

[10] KARPUZ, B.: Volterra theory on time scales, Results Math. 65 (2014), no. 3–4, 263–292. Search in Google Scholar

[11] KULIK, T.—TISDELL, C. C.: Volterra integral equations on time scales: basic qualitative and quantitative results with applications to initial value problems on unbounded domains, Int. J. Difference Equ. 3 (2008), no. 1, 103–133. Search in Google Scholar

[12] MESSINA, E.—VECCHIO, A.: Stability and Convergence of Solutions to Volterra Integral Equations on Time Scales, Discrete Dyn. Nat. Soc. 2015, Article ID 612156, 6 pp. Search in Google Scholar

[13] MIGDA, J.—MIGDA, M.: Asymptotic behavior of solutions of discrete volterra equations, Opuscula Math. 36 (2016), no. 1, 265–278. Search in Google Scholar

[14] MIGDA, M.—DUTKIEWICZ, A.: Asymptotic behavior of solutions of second-order difference equations of Volterra type,Turkish J. Math. 43 (2019), no. 5, 2203–2217. Search in Google Scholar

[15] MIGDA, M.—RŮŽIČKOVÁ, M.—SCHMEIDEL, E.: Boundedness and stability of discrete Volterra equations, Adv. Difference Equ. 47 (2015), 1–11. Search in Google Scholar

[16] OSTASZEWSKA, U.—SCHMEIDEL, E.—ZDANOWICZ, M.: Emergence of consensus of multi-agents systems on time scales, Miskolc Math. Notes 20, no. 2 (2019), 1201–1214. Search in Google Scholar

[17] SANTOS, I. L. D.: On Volterra integral equations on time scales, Mediterr. J. Math. 12 (2015), no. 2, 471–480. Search in Google Scholar

[18] SCHMEIDEL, E.—OSTASZEWSKA, U.—ZDANOWICZ, M.: Exponentially stable solution of mathematical model of agents dynamics on time scales, Adv. Difference Equ. 231 (2019), 1–19. Search in Google Scholar