Table of Contents
ISRN Mathematical Analysis
Volume 2011 (2011), Article ID 436045, 20 pages
http://dx.doi.org/10.5402/2011/436045
Research Article

Some Results for Nonlinear (𝑛+1)-Term Fractional Integrodifferential Inclusions with Multipoint Boundary Conditions

Department of Applied Mathematics, Donghua University, Shanghai 201620, China

Received 18 April 2011; Accepted 24 May 2011

Academic Editors: B. Djafari-Rouhani, G. L. Karakostas, and W. Kryszewski

Copyright Β© 2011 Huacheng Zhou et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We are concerned with the nonlinear (𝑛+1)-term fractional integrodifferential inclusions 𝐿(𝐷)π‘’βˆˆπΉ(𝑑,𝑒,𝑇𝑒,𝑆𝑒), π‘Ž.𝑒.π‘‘βˆˆ[0,1], where 𝐿(𝐷)=π·π›Όβˆ’π‘π‘›π·π›½π‘›βˆ’π‘π‘›βˆ’1π·π›½π‘›βˆ’1βˆ’β‹―βˆ’π‘1𝐷𝛽1, 0<𝛽1<𝛽2<β‹―<π›½π‘›βˆ’1<𝛽𝑛<1<𝛼<2, 𝑏1,𝑏2,…,𝑏𝑛 are constant coefficients, and ∫(𝑇𝑒)(𝑑)=10π‘˜(𝑑,𝑠)𝑒(𝑠)𝑑𝑠, ∫(𝑆𝑒)(𝑑)=𝑑0𝑙(𝑑,𝑠)𝑒(𝑠)𝑑𝑠, subject to the nonlocal conditions 𝑒(0)=0, βˆ‘π‘’(1)=π‘šπ‘–=1𝛾𝑖𝑒(πœ‚π‘–). The existence results are obtained by using two fixed-point theorems due to Bohnenblust-Karlin and Covitz-Nadler, respectively. Our results partly generalize and improve the known ones.