Abstract and Applied Analysis

Existence and Uniqueness of the Solutions for Fractional Differential Equations with Nonlinear Boundary Conditions

Xiping Liu, Fanfan Li, Mei Jia, and Ertao Zhi

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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.

Article information

Source
Abstr. Appl. Anal., Volume 2014 (2014), Article ID 758390, 11 pages.

Dates
First available in Project Euclid: 2 October 2014

Permanent link to this document
https://projecteuclid.org/euclid.aaa/1412277063

Digital Object Identifier
doi:10.1155/2014/758390

Mathematical Reviews number (MathSciNet)
MR3226230

Zentralblatt MATH identifier
07023028

Citation

Liu, Xiping; Li, Fanfan; Jia, Mei; Zhi, Ertao. Existence and Uniqueness of the Solutions for Fractional Differential Equations with Nonlinear Boundary Conditions. Abstr. Appl. Anal. 2014 (2014), Article ID 758390, 11 pages. doi:10.1155/2014/758390. https://projecteuclid.org/euclid.aaa/1412277063


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