Nonlocal nonlinear integrodifferential equations of fractional orders
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
Boundary Value Problems 2012, 2012:78 doi:10.1186/1687-2770-2012-78Published: 24 July 2012
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.