International Journal of Differential Equations
Volume 2012 (2012), Article ID 842813, 17 pages
http://dx.doi.org/10.1155/2012/842813
Research Article

Generalized Monotone Iterative Technique for Caputo Fractional Differential Equation with Periodic Boundary Condition via Initial Value Problem

J. D. Ramírez1 and A. S. Vatsala2

1Department of Mathematics, Lamar University, P.O. Box 10047, Beaumont, Texas 77710, USA
2Department of Mathematics, University of Louisiana Lafayette, P.O. Box 41010, Lafayette, LA 70504, USA

Received 23 May 2012; Revised 27 July 2012; Accepted 30 July 2012

Academic Editor: Shaher Momani

Copyright © 2012 J. D. Ramírez and A. S. Vatsala. 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 develop a generalized monotone method using coupled lower and upper solutions for Caputo fractional differential equations with periodic boundary conditions of order , where . We develop results which provide natural monotone sequences or intertwined monotone sequences which converge uniformly and monotonically to coupled minimal and maximal periodic solutions. However, these monotone iterates are solutions of linear initial value problems which are easier to compute.