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Abstract and Applied Analysis
Volume 2012 (2012), Article ID 512127, 16 pages
Positive Solutions of Eigenvalue Problems for a Class of Fractional Differential Equations with Derivatives
1School of Mathematical and Informational Sciences, Yantai University, Yantai, Shandong 264005, China
2School of Mathematical Sciences, Qufu Normal University, Qufu, Shandong 273165, China
3Department of Mathematics, Faculty of Science, Mahidol University, Bangkok 10400, Thailand
4Department of Mathematics and Statistics, Curtin University of Technology, Perth, WA 6845, Australia
Received 2 January 2012; Accepted 15 March 2012
Academic Editor: Shaoyong Lai
Copyright © 2012 Xinguang Zhang 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.
- I. Podlubny, Fractional Differential Equations, vol. 198 of Mathematics in Science and Engineering, Academic Press, San Diego, Calif, USA, 1999.
- S. G. Samko, A. A. Kilbas, and O. I. Marichev, Fractional Integrals and Derivatives, Theory and Applications, Gordon and Breach, Yverdon, Switzerland, 1993.
- K. S. Miller and B. Ross, An Introduction to the Fractional Calculus and Fractional Differential Equations, John Wiley & Sons, New York, NY, USA, 1993.
- 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.
- A. A. Kilbas and J. J. Trujillo, “Differential equations of fractional order: methods, results and problems. II,” Applicable Analysis, vol. 81, no. 2, pp. 435–493, 2002.
- 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.
- T. G. Bhaskar, V. Lakshmikantham, and S. Leela, “Fractional differential equations with a Krasnoselskii-Krein type condition,” Nonlinear Analysis, vol. 3, no. 4, pp. 734–737, 2009.
- M. ur Rehman and R. A. Khan, “Existence and uniqueness of solutions for multi-point boundary value problems for fractional differential equations,” Applied Mathematics Letters, vol. 23, no. 9, pp. 1038–1044, 2010.
- X. Zhang, L. Liu, and Y. Wu, “Multiple positive solutions of a singular fractional differential equation with negatively perturbed term,” Mathematical and Computer Modelling, vol. 55, no. 3-4, pp. 1263–1274, 2012.
- D. Jiang and C. Yuan, “The positive properties of the Green function for Dirichlet-type boundary value problems of nonlinear fractional differential equations and its application,” Nonlinear Analysis: Theory, Methods & Applications A, vol. 72, no. 2, pp. 710–719, 2010.
- X. Zhang and Y. Han, “Existence and uniqueness of positive solutions for higher order nonlocal fractional differential equations,” Applied Mathematics Letters, vol. 25, no. 3, pp. 555–560, 2012.
- C. S. Goodrich, “Existence of a positive solution to a class of fractional differential equations,” Applied Mathematics Letters, vol. 23, no. 9, pp. 1050–1055, 2010.
- C. S. Goodrich, “Existence of a positive solution to systems of differential equations of fractional order,” Computers & Mathematics with Applications, vol. 62, no. 3, pp. 1251–1268, 2011.
- M. El-Shahed and J. J. Nieto, “Nontrivial solutions for a nonlinear multi-point boundary value problem of fractional order,” Computers & Mathematics with Applications, vol. 59, no. 11, pp. 3438–3443, 2010.
- X. Zhang, L. Liu, and Y. Wu, “The eigenvalue problem for a singular higher order fractional differential equation involving fractional derivatives,” Applied Mathematics and Computation, vol. 218, no. 17, pp. 8526–8536, 2012.
- Y. Wang, L. Liu, and Y. H. Wu, “Positive solutions for a nonlocal fractional differential equation,” Nonlinear Analysis, vol. 74, no. 11, pp. 3599–3605, 2011.
- Y. Wang, L. Liu, and Y. H. Wu, “Positive solutions for a class of fractional boundary value problem with changing sign nonlinearity,” Nonlinear Analysis, vol. 74, no. 17, pp. 6434–6441, 2011.