Existence and Uniqueness of the Solutions for Fractional Differential Equations with Nonlinear Boundary Conditions. (19th June 2014)

• Record Type: Journal Article
• Authors: Liu, Xiping; Li, Fanfan; Jia, Mei; Zhi, Ertao
• Other Names: Bellouquid Abdelghani Academic Editor.
• Is Part Of: Abstract and applied analysis. Volume 2014(2014)
• Publication Date: 2014-06-19
• Subjects: Mathematical analysis -- Periodicals; Mathematical analysis; Applied Mathematics; Mathematical Analysis; Periodicals; 515.05
• DOI: 10.1155/2014/758390
• Languages: English
• ISSNs: 1085-3375

Abstract

Abstract : We study the existence and uniqueness of the solutions for the boundary value problem of fractional differential equations with nonlinear boundary conditions. By using the upper and lower solutions method in reverse order and monotone iterative techniques, we obtain the sufficient conditions of both the existence of the maximal and minimal solutions between an upper solution and a lower solution and the uniqueness of the solutions for the boundary value problem and present the iterative sequence for calculating the approximate analytical solutions of the boundary value problem and the error estimate. An example is also given to illustrate the main results.