Electronic Journal of Differential Equations, Vol. 2012 (2012), No. 100, pp. 1-13. Title: Method of upper and lower solutions for fractional differential equations Authors: Legang Lin (Univ. of Shanghai for Science and Tech., China) Xiping Liu (Univ. of Shanghai for Science and Tech., China) Haiqin Fang (Univ. of Shanghai for Science and Tech., China) Abstract: In this paper, we show the existence and uniqueness of solutions for the boundary-value problems of fractional differential equations, using the upper and lower solutions method and monotone iterative algorithm. An example is also included to illustrate our results. Submitted May 4, 2012. Published June 12, 2012. Math Subject Classifications: 34B15, 26A33. Key Words: Fractional differential equations; boundary-value problems; upper and lower solutions; monotone iterative algorithm.