Abstract and Applied Analysis

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

D. Baleanu, H. Mohammadi, and Sh. Rezapour

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Abstract

We investigate the existence and multiplicity of positive solutions for the nonlinear fractional differential equation initial value problem D 0 + α u ( t ) + D 0 + β u ( t ) = f ( t , u ( t ) ),  u ( 0 ) = 0 ,  0 < t < 1 , where 0 < β < α < 1 ,  D 0 + α is the standard Riemann-Liouville differentiation and f : [ 0,1 ] × [ 0 , ) [ 0 , ) 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

Permanent link to this document
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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