ArticleOriginal scientific text

Title

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

Authors 1, 2

Affiliations

  1. Department of Mathematics, Girls College of Education, P.O. Box 1011, Yanbu, Kingdom of Saudi Arabia
  2. Department of Mathematics, Faculty of Sciences, Alexandria University, Egypt

Abstract

In this paper, we study the existence of integrable solutions for the set-valued differential equation of fractional type (Dα-i=1n-1aiDαi)x(t)F(t,x(φ(t))), a.e. on (0,1), I1-αx(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.

Keywords

fractional calculus, set-valued problem

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Pages:
83-93
Main language of publication
English
Received
2006-10-28
Published
2008
Exact and natural sciences