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Existence results for random fractional differential equations

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
In this paper, an existence result for a random fractional differential equation is established under a Carathéodory condition. Existence results for extremal random solutions are also proved. Finally, an existence and uniqueness result is given.
Rocznik
Strony
813--825
Opis fizyczny
Bibliogr. 25 poz.
Twórcy
autor
  • Constantin Brancusi University Targu-Jiu, Romania
autor
  • School of Mathematics Statistics and Applied Mathematics National University of Ireland Galway, Ireland
autor
  • Abdus Salam School of Mathematical Sciences GC University Lahore, Pakistan
Bibliografia
  • [1] W. Arendt, C.J.K. Batty, M. Hiber, F. Neubrander, Vector-valued Laplace Transforms and Cauchy Problems, Monographs in Mathematics, Vol. 96, Birkhäuser, Basel, 2011.
  • [2] P. Billingsley, Weak Convergence of Measures: Applications in Probability, CBMS-NSF Regional Conference Series in Applied Mathematics, SIAM, Philadelphia, 1971.
  • [3] A.T. Bharucha-Reid, Random Integral Equations, Academic Press, New York, 1972.
  • [4] K. Diethelm, The Analysis of Fractional Differential Equations, Springer, Braunschweig, Germany, 2004.
  • [5] B.C. Dhage, S.K. Ntouyas, Existence and attractivity results for nonlinear first order random differential equations, Opuscula Math. 30 (2010) 4, 411–429.
  • [6] B.C. Dhage, On global existence and attractivity results for nonlinear random integral equations, Panamer. Math. J. 19 (2009) 1, 97–111.
  • [7] B.C. Dhage, On n-th order nonlinear ordinary random differential equations, Nonlinear Oscil. 13 (2011) 4, 535–549.
  • [8] R.M. Dudley, Real Analysis and Probability, Vol. 74 of Cambridge Studies in Advanced Mathematics, Cambridge University Press, Cambridge, 2002.
  • [9] R. Edsinger, Random Ordinary Differential Equations, Ph.D. Thesis, Univ. of California, Berkeley, 1968.
  • [10] C.J. Himmelberg, Measurable relations, Fund. Math. 87 (1975), 53–72.
  • [11] O. Kallenberg, Foundations of Modern Probability, 2nd ed., Springer-Verlag, New York, 2002.
  • [12] A.A. Kilbas, H.M. Srivastava, J.J. Trujillo, Theory and Applications of Fractional Differential Equations, North-Holland Mathematics Studies, Vol. 204, Elsevier Science B.V., Amsterdam, 2006.
  • [13] G.S. Ladde, V. Lakshmikantham, Random Differential Inequalities, Academic Press, New York, 1980.
  • [14] V. Lakshmikantham, A.S. Vatsala, Theory of fractional differential inequalities and applications, Commun. Appl. Anal. 11 (2007), 395–402.
  • [15] V. Lakshmikantham, A.S. Vatsala, Basic theory of fractional differential equations, Nonlinear Anal. 69 (2008), 2677–2682.
  • [16] C. Lungan, V. Lupulescu, Random differential equations on time scales, Electron. J. Differential Equations Vol. 2012 (2012), no. 86, 1–14.
  • [17] V. Lupulescu, S.K. Ntouyas, Random fractional differential equations, International Electronic Journal of Pure and Applied Mathematics, 4 (2012) 2, 119–136.
  • [18] V. Lupulescu, C. Lungan, Random integral equations on time scales, Opuscula Math. 33 (2013) 2, 323–335.
  • [19] K.S. Miller, B. Ross, An Introduction to the Fractional Calculus and Fractional Differential Equations, Wiley, New York, 1993.
  • [20] Y.V. Prohorov, Convergence of Random Processes and Limit Theorems in Probability Theory, Theor. Probability Appl. 1 (1956) 2, 157–214.
  • [21] S.G. Samko, A.A. Kilbas, O.I. Marichev, Fractional Integrals and Derivatives. Theory and Applications, Gordon and Breach, Yverdon, 1993.
  • [22] T.T. Soong, Random Differential Equations in Science and Engineering, Academic Press, New York, 1973.
  • [23] J.L. Strand, Random Ordinary Differential Equations, J. Differential Equations 7 (1970), 538–553.
  • [24] J.L. Strand, Stochastic Ordinary Differential Eqnations, Ph. D. Thesis, Univ. of California, Berkeley, 1968.
  • [25] C.P. Tsokos, W.J. Padgett, Random Integral Equations with Applications to Life Sciences and Engineering, Academic Press, New York, 1974.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-97dd5776-3827-4916-9ac0-95be9a499ac4
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