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2012 Existence and Uniqueness of Solutions for Initial Value Problem of Nonlinear Fractional Differential Equations
Qiuping Li, Shurong Sun, Ping Zhao, Zhenlai Han
Abstr. Appl. Anal. 2012(SI01): 1-14 (2012). DOI: 10.1155/2012/615230

Abstract

We discuss the initial value problem for the nonlinear fractional differential equation L ( D ) u = f ( t , u ) , t ( 0,1 ] , u ( 0 ) = 0 , where L ( D ) = D s n - a n - 1 D s n - 1 - - a 1 D s 1 , 0 < s 1 < s 2 < < s n < 1 , and a j < 0 , j = 1,2 , , n - 1 , D s j is the standard Riemann-Liouville fractional derivative and f : [ 0,1 ] × is a given continuous function. We extend the basic theory of differential equation, the method of upper and lower solutions, and monotone iterative technique to the initial value problem. Some existence and uniqueness results are established.

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Qiuping Li. Shurong Sun. Ping Zhao. Zhenlai Han. "Existence and Uniqueness of Solutions for Initial Value Problem of Nonlinear Fractional Differential Equations." Abstr. Appl. Anal. 2012 (SI01) 1 - 14, 2012. https://doi.org/10.1155/2012/615230

Information

Published: 2012
First available in Project Euclid: 5 April 2013

zbMATH: 1247.35189
MathSciNet: MR2947733
Digital Object Identifier: 10.1155/2012/615230

Rights: Copyright © 2012 Hindawi

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Vol.2012 • No. SI01 • 2012
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