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2008 | 28 | 1 | 83-93
Tytuł artykułu

Set-valued fractional order differential equations in the space of summable functions

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Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
In this paper, we study the existence of integrable solutions for the set-valued differential equation of fractional type
$(D^{αₙ} - ∑_{i=1}^{n-1} a_i D^{α_i})x(t) ∈ F(t,x(φ(t)))$,
a.e. on (0,1), $I^{1 - αₙ} x(0) = c$, αₙ ∈ (0,1),
where F(t,·) is lower semicontinuous from ℝ into ℝ and F(·,·) is measurable. The corresponding single-valued problem will be considered first.
Słowa kluczowe
Twórcy
  • Department of Mathematics, Girls College of Education, P.O. Box 1011, Yanbu, Kingdom of Saudi Arabia
  • Department of Mathematics, Faculty of Sciences, Alexandria University, Egypt
Bibliografia
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  • [4] V. Daftardar-Gejji, Positive solutions of a system of non-autonomous fractional differential equations, J. Math. Anal. Appl. 302 (2005), 56-64.
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  • [9] A.M.A. El-Sayed and A.G. Ibrahim, Multivalued fractional differential equations, Appl. Math. Comput. 68 (1995), 15-25.
  • [AAA] A.M.A. El-Sayed and A.G. Ibrahim, Definite integral of fractional order for set-valued functions, J. Frac. Calculus 11 (1996), 15-25.
  • [11] A.M.A. El-Sayed, Nonlinear functional differential equations of arbitrary order, Nonlinear Anal. 33 (2) (1998), 181-186.
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  • [kil] A.A. Kilbas and J.J. Trujillo, Differential equations of fractional order: methods, results and problems, I, Appl. Anal. 78 (2001), 153-192.
  • [kst] A.A. Kilbas, H.M. Srivastava and J.J Trujillo, Theory and Applications of Fractional Differential Equations, Amsterdam, 2006.
  • [16] K.S. Miller and B. Ross, An Introduction to the Fractional Calculus and Differential Equations, John Wiley, New York, 1993.
  • [17] K. Przesławski and L.E. Rybiński, Michael selection theorem under weak lower semicontinuity assumption, Proc. Amer. Math. Soc. 109 (1990), 537-543.
  • [18] D. Repovs and P.V. Semenov, Continuous Selection of Multivalued Mappings, Kluwer Academic Press, 1998.
  • [19] S. Samko, A. Kilbas and O. Marichev, Fraction Integrals and Drivatives, Gordon and Breach Science Publisher, 1993.
  • [sz] J.-P. Sun and Y.-H. Zhao, Multiplicity of positive solutions of a class of nonlinear fractional differential equations, J. Computer and Math. Appl. 49 (2005), 73-80.
  • [20] C. Swartz, Measure, Integration and Function Spaces, World Scientific, Singapore, 1994.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-doi-10_7151_dmdico_1096
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