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

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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: D q x(t)=Ax(t)+t n f(t,x(t),Bx(t)), t∈[0,T], n∈ℤ+, x(0)+g(x)=x 0, where 0<q<1, A is the infinitesimal generator of a C 0-semigroup of bounded linear operators on a Banach space X.

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Authors and Affiliations

  1. Département de Mathématiques et Informatique, Université des Antilles et de la Guadeloupe, Campus Fouillole, 97159, Pointe-à-Pitre, Guadeloupe (FWI), France

    G. M. Mophou

  2. Department of Mathematics, Morgan State University, 1700 E. Cold Spring Lane, Baltimore, MD, 21251, USA

    G. M. N’Guérékata

Authors
  1. G. M. Mophou
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  2. G. M. N’Guérékata
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Correspondence to G. M. N’Guérékata.

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Communicated by Jerome A. Goldstein.

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Mophou, G.M., N’Guérékata, G.M. Existence of the mild solution for some fractional differential equations with nonlocal conditions. Semigroup Forum 79, 315–322 (2009). https://doi.org/10.1007/s00233-008-9117-x

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  • DOI: https://doi.org/10.1007/s00233-008-9117-x

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