Existence and Uniqueness of Solutions for Initial Value Problem of Nonlinear Fractional Differential Equations
- Qiuping Li
- Shurong Sun
- Ping Zhao
- Zhenlai Han
Publication date
January 2012
DOI Publisher
Hindawi Limited Journal
Abstract and Applied AnalysisAbstract
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)=Dsn-an-1Dsn-1-⋯-a1Ds1, 0<s1<s2<⋯<sn<1, and aj<0, j=1,2,…,n-1, Dsj is the standard Riemann-Liouville fractional derivative and f:[0,1]×ℝ→ℝ 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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