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Tytuł artykułu

On fractional random differential equations with delay

Treść / Zawartość
Identyfikatory
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
In this paper, we consider the existence and uniqueness of solutions of the fractional random differential equations with delay. Moreover, some kind of boundedness of the solution is proven. Finally, the applicability of the theoretical results is illustrated with some real world examples.
Rocznik
Strony
541--556
Opis fizyczny
Bibliogr. 28 poz.
Twórcy
autor
  • Banking University Faculty of Economic Mathematics Ho Chi Minh City, Vietnam
autor
autor
Bibliografia
  • [1] W. Arendt, K. Batty, M. Hiber, F. Neubrander, Vector-valued Laplace Transforms and Cauchy Problems, Monographs in Mathematics, Vol. 96, Birkhauser, Basel, 2011.
  • [2] M. Benchohra, J. Henderson, S.K. Ntouyas, A. Ouahab, Existence results for fractional order functional differential equations with infinite delay, J. Math. Anal. Appl. 338 (2008), 1340-1350.
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  • [4] J. Deng, L. Ma, Existence and uniqueness of solutions of initial value problems for nonlinear fractional differential equations, App. Math Lett. 6 (2010), 676-680.
  • [5] J. Deng, H. Qu, New uniqueness results of solutions for fractional differential equations with infinite delay, Comput. Math. Appl. 60 (2010), 2253-2259.
  • [6] B.C. Dhage, Monotone iterative technique for Caratheodory theorem of nonlinear functional random integral equations, Tamkang J. Math. 35 (2002), 341-351.
  • [7] B.C. Dhage, Some algebraic and topological random fixed point theorem with applications to nonlinear random integral quations, Tamkang J. Math. 35 (2004), 321-345.
  • [8] B.C. Dhage, A random version of a Schaefer type fixed point theorem with applications to functional random integral equations, Tamkang J. Math. 35 (2004), 197-205.
  • [9] B.C. Dhage, S.V. Badgire, S.K. Ntouyas, Periodic boundary value problems of second order random, differential equations, Electron. J. Qual. Theory Differ. Equ. 21 (2009), 1-14.
  • [10] S.S. Dragomir, R.P. Agarwal, N.S. Barnett, Inequalities for Beta and Gamma functions via some classical and new integral inequalities, J. Inequal. Appl. 5 (2000), 103-165.
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  • [12] X. Han, X. Ma, G. Dai, Solutions to fourth-order random, differential equations with, periodic boundary conditions, Electron. J. Differential Equations 235 (2012), 1-9.
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  • [14] S. Itoh, Random fixed point theorems with applications to random differential equations in Banach spaces, J. Math. Anal. Appl. 67 (1979), 261-273.
  • [15] O. Kallenberg, Foundations of Modern Probability, 2nd ed. Springer-Verlag, New York, 2002.
  • [16] A.A. Kilbas, H.M. Srivastava, J.J. Trujillo, Theory and Applications of Fractional Differential Equations, North-Holland Mathematics Studies, Vol. 204, 2006.
  • [17] G.S. Ladde, V. Lakshmikantham, Random Differential Inequalities, Academic Press, New York, 1980.
  • [18] V. Lakshmikantham, Theory of fractional functional differential equations, Nonlinear Analysis: TMA, 69 (2008) 10, 3337-3343.
  • [19] V. Lakshmikantham, A.S. Vatsala, Theory of fractional differential inequalities and applications, Commun. Math. Anal. 2 (2007), 395-402.
  • [20] V. Lakshmikantham, A.S. Vatsala, Basic theory of fractional differential equations, Nonlinear Anal. 69 (2008), 2677-2682.
  • [21] V. Lakshmikantham, A.S. Vatsala, General uniqueness and monotone iterative technique for fractional differential equations, App. Math. Lett. 21 (2008), 828-834.
  • [22] V. Lupulescu, C. Lungan, Random, dynamical systems on time scales, Electron. J. Differential Equations 86 (2012), 1-14.
  • [23] V. Lupulescu, C. Lungan, Random integral equation on time scales, Opuscula Math. 33 (2013), 323-335.
  • [24] V. Lupulescu, S.K. Ntouyas, Random fractional differential equations, Int. Electron. J. Pure Appl. Math. 4 (2012), 119-136.
  • [25] V. Lupulescu, D. O'Regan, Ghaus ur Rahman, Existence results for random fractional differential equations, Opuscula Math. 34 (2014) 4, 813-825.
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Uwagi
Opracowanie ze środków MNiSW w ramach umowy 812/P-DUN/2016 na działalność upowszechniającą naukę.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-dab2d85f-ce93-4608-9b6c-189160919e79
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