Semigroup Forum

, Volume 79, Issue 2, pp 315–322 | Cite as

Existence of the mild solution for some fractional differential equations with nonlocal conditions

Research article

Abstract

We are concerned in this paper with the existence of mild solutions to the Cauchy Problem for the fractional differential equation with nonlocal conditions: Dqx(t)=Ax(t)+tnf(t,x(t),Bx(t)), t∈[0,T], n∈ℤ+, x(0)+g(x)=x0, where 0<q<1, A is the infinitesimal generator of a C0-semigroup of bounded linear operators on a Banach space X.

Keywords

Cauchy problem Fractional abstract differential equation Nonlocal conditions Semigroup of bounded operators 

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Copyright information

© Springer Science+Business Media, LLC 2008

Authors and Affiliations

  1. 1.Département de Mathématiques et InformatiqueUniversité des Antilles et de la GuadeloupeGuadeloupe (FWI)France
  2. 2.Department of MathematicsMorgan State UniversityBaltimoreUSA

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