Abstract and Applied Analysis
Volume 2011 (2011), Article ID 968735, 18 pages
http://dx.doi.org/10.1155/2011/968735
Research Article

Perturbation Results and Monotone Iterative Technique for Fractional Evolution Equations

Jia Mu

Department of Mathematics, Northwest Normal University, Lanzhou, Gansu 730000, China

Received 18 April 2011; Revised 17 May 2011; Accepted 4 July 2011

Academic Editor: Victor M. Perez Garcia

Copyright © 2011 Jia Mu. 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 mainly study the fractional evolution equation in an ordered Banach space 𝑋 𝐶 𝐷 𝑎 0 + 𝑢 ( 𝑡 ) + 𝐴 𝑢 ( 𝑡 ) = 𝑓 ( 𝑡 , 𝑢 ( 𝑡 ) , 𝐺 𝑢 ( 𝑡 ) ) , 1 < 𝛼 < 2 , 𝑢 ( 0 ) = 𝑥 ∈ 𝑋 , 𝑢 ( 0 ) = 𝜃 . Using the monotone iterative technique based on lower and upper solutions, the existence and uniqueness results are obtained. The necessary perturbation results for accomplishing this approach are also developed.