Existence and uniqueness of solutions of differential equations of fractional order with integral boundary conditions

Abstract

Recently, Wang and Xie [T. Wang, F. Xie, J. Nonlinear Sci. Appl., 1 (2009), 206–212] developed monotone iterative method for Riemann-Liouville fractional differential equations with integral boundary conditions with the strong hypothesis of locally H¨older continuity and obtained existence and uniqueness of a solution for the problem. In this paper, we apply the comparison result without locally H¨older continuity due to Vasundhara Devi to develop monotone iterative method for the problem and obtain existence and uniqueness of a solution of the problem. c 2014 All rights reserved.