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Abstract and Applied Analysis
Volume 2012 (2012), Article ID 826580, 15 pages
doi:10.1155/2012/826580
Research Article
Positive and Nondecreasing Solutions to an m-Point Boundary Value Problem for Nonlinear Fractional Differential Equation
Departamento de Matemáticas, Universidad de Las Palmas de Gran Canaria, Campus de Tafira Baja, 35017 Las Palmas de Gran Canaria, Spain
Received 30 September 2011; Accepted 15 November 2011
Academic Editor: Shaher M. Momani
Copyright © 2012 I. J. Cabrera et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Linked References
- L. M. B. C. Campos, “On the solution of some simple fractional differential equations,” International Journal of Mathematics and Mathematical Sciences, vol. 13, no. 3, pp. 481–496, 1990. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
- K. S. Miller and B. Ross, An Introduction to the Fractional Calculus and Fractional Differential Equations, John Wiley & Sons, New York, NY, USA, 1993.
- L. Yi and D. Shusen, “A class of analytic functions defined by fractional derivation,” Journal of Mathematical Analysis and Applications, vol. 186, no. 2, pp. 504–513, 1994. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
- D. Delbosco and L. Rodino, “Existence and uniqueness for a nonlinear fractional differential equation,” Journal of Mathematical Analysis and Applications, vol. 204, no. 2, pp. 609–625, 1996. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
- M. El-Shahed, “Positive solutions for boundary value problem of nonlinear fractional differential equation,” Abstract and Applied Analysis, Article ID 10368, 8 pages, 2007. View at Zentralblatt MATH
- S. Liang and J. Zhang, “Positive solutions for boundary value problems of nonlinear fractional differential equation,” Nonlinear Analysis, vol. 71, no. 11, pp. 5545–5550, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
- J. Caballero, J. Harjani, and K. Sadarangani, “Existence and uniqueness of positive solution for a boundary value problem of fractional order,” Abstract and Applied Analysis, Article ID 165641, 12 pages, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
- W. Zhong, “Positive solutions for multipoint boundary value problem of fractional differential equations,” Abstract and Applied Analysis, Article ID 601492, 15 pages, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
- S. Liang and J. Zhang, “Existence and uniqueness of positive solutions to m-point boundary value problem for nonlinear fractional differential equation,” Journal of Applied Mathematics and Computing. In press. View at Publisher · View at Google Scholar
- A. Amini-Harandi and H. Emami, “A fixed point theorem for contraction type maps in partially ordered metric spaces and application to ordinary differential equations,” Nonlinear Analysis, vol. 72, no. 5, pp. 2238–2242, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
- J. Harjani and K. Sadarangani, “Fixed point theorems for weakly contractive mappings in partially ordered sets,” Nonlinear Analysis, vol. 71, no. 7-8, pp. 3403–3410, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
- J. J. Nieto and R. Rodríguez-López, “Contractive mapping theorems in partially ordered sets and applications to ordinary differential equations,” Order, vol. 22, no. 3, pp. 223–239, 2005. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
- D. O'Regan and A. Petruşel, “Fixed point theorems for generalized contractions in ordered metric spaces,” Journal of Mathematical Analysis and Applications, vol. 341, no. 2, pp. 1241–1252, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
- A. A. Kilbas and J. J. Trujillo, “Differential equations of fractional order: methods, results and problems. I,” Applicable Analysis, vol. 78, no. 1-2, pp. 153–192, 2001. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
- S. G. Samko, A. A. Kilbas, and O. I. Marichev, Fractional Integrals and Derivatives. Theory and applications, Gordon and Breach Science Publishers, Yverdon, Switzerland, 1993.
- Z. Bai and H. Lü, “Positive solutions for boundary value problem of nonlinear fractional differential equation,” Journal of Mathematical Analysis and Applications, vol. 311, no. 2, pp. 495–505, 2005. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
- A. A. Kilbas, H. M. Srivastava, and J. J. Trujillo, Theory and Applications of Fractional Differential Equations, vol. 204 of North-Holland Mathematics Studies, Elsevier Science B.V., Amsterdam, The Netherlands, 2006.
- J. Caballero Mena, J. Harjani, and K. Sadarangani, “Existence and uniqueness of positive and nondecreasing solutions for a class of singular fractional boundary value problems,” Boundary Value Problems, Article ID 421310, 10 pages, 2009. View at Zentralblatt MATH
- J. Harjani and K. Sadarangani, “Fixed point theorems for weakly contractive mappings in partially ordered sets,” Nonlinear Analysis, vol. 71, no. 7-8, pp. 3403–3410, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
- J. Caballero, J. Harjani, and K. Sadarangani, “Uniqueness of positive solutions for a class of fourth-order boundary value problems,” Abstract and Applied Analysis, Article ID 543035, 13 pages, 2011. View at Zentralblatt MATH