Abstract and Applied Analysis

Lower and Upper Solutions Method for Positive Solutions of Fractional Boundary Value Problems

R. Darzi, B. Mohammadzadeh, A. Neamaty, and D. Bǎleanu

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Abstract

We apply the lower and upper solutions method and fixed-point theorems to prove the existence of positive solution to fractional boundary value problem D 0 + α u t + f t , u t = 0 , 0 < t < 1 , 2 < α 3 , u 0 = u 0 = 0 , D 0 + α 1 u 1 = β u ξ , 0 < ξ < 1 , where D 0 + α denotes Riemann-Liouville fractional derivative, β is positive real number, β ξ α 1 2 Γ α , and f is continuous on 0,1 × 0 , . As an application, one example is given to illustrate the main result.

Article information

Source
Abstr. Appl. Anal., Volume 2013, Special Issue (2013), Article ID 847184, 7 pages.

Dates
First available in Project Euclid: 26 February 2014

Permanent link to this document
https://projecteuclid.org/euclid.aaa/1393450397

Digital Object Identifier
doi:10.1155/2013/847184

Mathematical Reviews number (MathSciNet)
MR3096828

Zentralblatt MATH identifier
07095425

Citation

Darzi, R.; Mohammadzadeh, B.; Neamaty, A.; Bǎleanu, D. Lower and Upper Solutions Method for Positive Solutions of Fractional Boundary Value Problems. Abstr. Appl. Anal. 2013, Special Issue (2013), Article ID 847184, 7 pages. doi:10.1155/2013/847184. https://projecteuclid.org/euclid.aaa/1393450397


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