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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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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
  • 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
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