Open Access Research

Nonlocal nonlinear integrodifferential equations of fractional orders

Amar Debbouche1, Dumitru Baleanu2,3* and Ravi P Agarwal4

Author Affiliations

1 Department of Mathematics, Faculty of Science, Guelma University, Guelma, Algeria

2 Department of Mathematics and Computer Science, Cankaya University, Ankara, Turkey

3 Institute of Space Sciences, P.O. Box MG-23, Magurele-Bucharest, RO, 76900, Romania

4 Department of Mathematics, Texas A&M University, Kingsville, TX, 78363, USA

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Boundary Value Problems 2012, 2012:78 doi:10.1186/1687-2770-2012-78

Published: 24 July 2012

Abstract

In this paper, Schauder fixed point theorem, Gelfand-Shilov principles combined with semigroup theory are used to prove the existence of mild and strong solutions for nonlinear fractional integrodifferential equations of Sobolev type with nonlocal conditions in Banach spaces. To illustrate our abstract results, an example is given.

MSC: 35A05, 34G20, 34K05, 26A33.

Keywords:
fractional evolution equation; nonlocal condition; Schauder’s fixed point theorem; uniformly continuous semigroup