## Abstract and Applied Analysis

### Positive Solutions of an Initial Value Problem for Nonlinear Fractional Differential Equations

#### Abstract

We investigate the existence and multiplicity of positive solutions for the nonlinear fractional differential equation initial value problem ${D}_{0+}^{\alpha }u(t)+{D}_{0+}^{\beta }u(t)=f(t,u(t)),$ $u(0)=0, 0, where $0<\beta <\alpha <1, {D}_{0+}^{\alpha }$ is the standard Riemann-Liouville differentiation and $f:[0,1]{\times}[0,\infty )\to [0,\infty )$ is continuous. By using some fixed-point results on cones, some existence and multiplicity results of positive solutions are obtained.

#### Article information

Source
Abstr. Appl. Anal., Volume 2012, Special Issue (2012), Article ID 837437, 7 pages.

Dates
First available in Project Euclid: 5 April 2013

https://projecteuclid.org/euclid.aaa/1365168365

Digital Object Identifier
doi:10.1155/2012/837437

Mathematical Reviews number (MathSciNet)
MR2935139

Zentralblatt MATH identifier
1242.35215

#### Citation

Baleanu, D.; Mohammadi, H.; Rezapour, Sh. Positive Solutions of an Initial Value Problem for Nonlinear Fractional Differential Equations. Abstr. Appl. Anal. 2012, Special Issue (2012), Article ID 837437, 7 pages. doi:10.1155/2012/837437. https://projecteuclid.org/euclid.aaa/1365168365

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