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Abstrakty
In this paper, we present the existence and uniqueness of random solution of a random integral equation of Volterra type on time scales. We also study the asymptotic properties of the unique random solution.
Słowa kluczowe
Czasopismo
Rocznik
Tom
Strony
323--335
Opis fizyczny
Bibliogr. 28 poz.
Twórcy
autor
- Constantin Brancusi University Targu-Jiu, Romania
autor
- Gheorghe Tatarascu School of Targu Jiu 23 August 47, Romania
Bibliografia
- [1] M. Adivar, N.Y. Raffoul, Existence results for periodic solutions of integro-dynamic equations on time scales, Ann. Mat. Pura Appl. 188 (2009) 4, 543-559.
- [2] R. Agarwal, M. Bohner, D. O'Regan, A. Peterson, Dynamic equations on time scales: a survey, J. Comput. Appl. Math. 141 (2002), 1-26.
- [3] B. Aulbach, L. Neidhart, Integration on measure chains, Proc. of the Sixth International Conference on Difference Equations, B. Aulbach, S. Elaydi, G. Ladas, eds., Augsburg, Germany 2001, pp. 239-252.
- [4] M. Bohner, A. Peterson, Dynamic Equations on Time Scales: an Introduction with Applications, Birkhauser, Boston, 2001.
- [5] M. Bohner, A. Peterson, Advances in Dynamic Equations on Time Scales, Birkhauser, Boston, 2003.
- [6] E. Akin-Bohner, M. Bohner, F. Akin, Pachpatte inequalities on time scales, JIPAM. J. Inequal. Pure Appl. Math. 6 (2005) 1, 1-23.
- [7] N.U. Ahmed, K.L. Teo, On the stability of a class of nonlinear stochastic systems, J. Information and Control 20 (1972), 276-293.
- [8] T.A. Burton, Volterra integral and differential equations, vol. 202 of Mathematics in Science and Engineering, Elsevier B.V., Amsterdam, 2nd ed., 2005.
- [9] A. Cabada, D.R. Vivero, Expression of the Lebesgue A-integral on time scales as a usual Lebesgue integral; application to the calculus of A-antiderivatives, Math. Comput. Modelling 43 (2006), 194-207.
- [10] M. Cichoń, On integrals of vector-valued functions on time scales, Commun. Math. Anal. 1 (2011) 11, 94-110.
- [11] C. Corduneanu, Integral Equations and Stability of Feedback Systems, Academic Press. New York-London, 1973.
- [12] B.C. Dhage, S.K. Ntouyas, Existence and attractivity results for nonlinear first order random differential equations, Opuscula Math. 30 (2010) 4, 411-429.
- [13] N. Dunford, J.T. Schwartz, Linear Operators I, Interscience, New York, 1958.
- [14] G.Sh. Guseinov, Integration on time scales, J. Math. Anal. Appl. 285 (2003), 107-127.
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- [16] T. Kulik, C.C. Tisdell, 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) 1, 103-133.
- [17] J.L. Massera, J.J. Schaffer, Linear Differential Equations and Function Spaces, Academic Press, New York, 1966.
- [18] L. Neidhart, Integration im Rahmen des Mafikettenkalkuls, Diploma Thesis, University of Augsburg, 2001.
- [19] A. Sikorska-Nowak, Integrodifferential equations on time scales with Henstock-Kurzweil-Pettis delta integrals, Abstr. Appl. Anal. 1 (2010), 1-17.
- [20] D.B. Pachpatte, On a nonstandard Volterra type dynamic integral equation on time scales, Electron. J. Qual. Theory Differ. Equ. 72 (2009), 1-14.
- [21] W.J. Padnett, C.P. Tsokos, On a stochastic integro-differential equation of Volterra type, SIAM J. Appl. Math. 23 (1972), 499-512.
- [22] A.T. Bharucha-Reid, Random Integral Equations, Academic Press, New York, 1972.
- [23] S. Sanyal, Mean square stability of ltd Volterra dynamic equation, Nonlinear Dyn. Syst. Theory 11 (2011) 1, 83-92.
- [24] S. Sanyal, Stochastic Dynamic Equations, Ph.D. Thesis, Missouri University of Science and Technology, Rolla, Missouri, 2008.
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Typ dokumentu
Bibliografia
Identyfikator YADDA
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