Abstract and Applied Analysis

The Existence and Uniqueness of a Class of Fractional Differential Equations

Zhanbing Bai, Sujing Sun, and YangQuan Chen

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Abstract

By using inequalities, fixed point theorems, and lower and upper solution method, the existence and uniqueness of a class of fractional initial value problems, D 0 + q x ( t ) = f ( t , x ( t ) ,   D 0 + q - 1 x ( t ) ) ,   t ( 0 , T ) ,   x ( 0 ) = 0 ,   D 0 + q - 1 x ( 0 ) = x 0 ,  are discussed, where f C ( [ 0 , T ] × R 2 , R ) , D 0 + q x ( t ) is the standard Riemann-Liouville fractional derivative, 1 < q < 2 . Some mistakes in the literature are pointed out and some new inequalities and existence and uniqueness results are obtained.

Article information

Source
Abstr. Appl. Anal., Volume 2014 (2014), Article ID 486040, 6 pages.

Dates
First available in Project Euclid: 2 October 2014

Permanent link to this document
https://projecteuclid.org/euclid.aaa/1412277058

Digital Object Identifier
doi:10.1155/2014/486040

Mathematical Reviews number (MathSciNet)
MR3226199

Zentralblatt MATH identifier
07022469

Citation

Bai, Zhanbing; Sun, Sujing; Chen, YangQuan. The Existence and Uniqueness of a Class of Fractional Differential Equations. Abstr. Appl. Anal. 2014 (2014), Article ID 486040, 6 pages. doi:10.1155/2014/486040. https://projecteuclid.org/euclid.aaa/1412277058


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