Existence and Uniqueness of Positive Solutions for a Singular Fractional Three-Point Boundary Value Problem. (21st August 2012)

• Record Type: Journal Article
• Authors: Cabrera, I. J.; Harjani, J.; Sadarangani, K. B.
• Other Names: Trujillo Juan J. Academic Editor.
• Is Part Of: Abstract and applied analysis. Volume 2012(2012)
• Publication Date: 2012-08-21
• Subjects: Mathematical analysis -- Periodicals; Mathematical analysis; Applied Mathematics; Mathematical Analysis; Periodicals; 515.05
• DOI: 10.1155/2012/803417
• Languages: English
• ISSNs: 1085-3375

Abstract

Abstract : We investigate the existence and uniqueness of positive solutions for the following singular fractional three-point boundary value problemD 0 + α u ( t ) + f ( t, u ( t ) ) = 0, 0 < t < 1, u ( 0 ) = u ′ ( 0 ) = u ′′ ( 0 ) = 0, u ′′ ( 1 ) = β u ′′ ( η ), where3 < α ≤ 4, D 0 + α is the standard Riemann-Liouville derivative andf : ( 0, 1 ] × [ 0, ∞ ) → [ 0, ∞ ) withlim t → 0 + f ( t, · ) = ∞ (i.e., f is singular att = 0 ). Our analysis relies on a fixed point theorem in partially ordered metric spaces.