Abstract and Applied Analysis

Positive Solutions for Boundary Value Problem of Nonlinear Fractional Differential Equation

Moustafa El-Shahed

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We are concerned with the existence and nonexistence of positive solutions for the nonlinear fractional boundary value problem: D 0 + α u ( t ) + λ a ( t )  f ( u ( t ) ) = 0 ,  0 < t < 1 ,  u ( 0 ) = u ( 0 ) = u ( 1 ) = 0 , where 2 < α < 3 is a real number and D 0 + α is the standard Riemann-Liouville fractional derivative. Our analysis relies on Krasnoselskiis fixed point theorem of cone preserving operators. An example is also given to illustrate the main results.

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Abstr. Appl. Anal., Volume 2007 (2007), Article ID 10368, 8 pages.

First available in Project Euclid: 27 February 2008

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El-Shahed, Moustafa. Positive Solutions for Boundary Value Problem of Nonlinear Fractional Differential Equation. Abstr. Appl. Anal. 2007 (2007), Article ID 10368, 8 pages. doi:10.1155/2007/10368. https://projecteuclid.org/euclid.aaa/1204126601

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