- About this Journal ·
- Abstracting and Indexing ·
- Aims and Scope ·
- Annual Issues ·
- Article Processing Charges ·
- Author Guidelines ·
- Bibliographic Information ·
- Citations to this Journal ·
- Contact Information ·
- Editorial Board ·
- Editorial Workflow ·
- Free eTOC Alerts ·
- Publication Ethics ·
- Recently Accepted Articles ·
- Reviewers Acknowledgment ·
- Submit a Manuscript ·
- Subscription Information ·
- Table of Contents
Abstract and Applied Analysis
Volume 2013 (2013), Article ID 162418, 7 pages
Positive Solutions Using Bifurcation Techniques for Boundary Value Problems of Fractional Differential Equations
School of Mathematical Sciences, Shandong Normal University, Jinan 250014, China
Received 3 April 2013; Accepted 30 September 2013
Academic Editor: Soheil Salahshour
Copyright © 2013 Yansheng Liu. 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.
- B. Ahmad and J. J. Nieto, “Existence of solutions for nonlocal boundary value problems of higher-order nonlinear fractional differential equations,” Abstract and Applied Analysis, vol. 2009, Article ID 494720, 9 pages, 2009.
- K. Diethelm, The Analysis of Fractional Differential Equations: An Application-Oriented Exposition Using Differential Operators of Caputo Type, vol. 2004, Springer, Berlin, Germany, 2010.
- 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.
- 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 Integral and Derivatives (Theory and Applications), Gordon and Breach, Yverdon, Switzerland, 1993.
- Z. Wei, Q. Li, and J. Che, “Initial value problems for fractional differential equations involving Riemann-Liouville sequential fractional derivative,” Journal of Mathematical Analysis and Applications, vol. 367, no. 1, pp. 260–272, 2010.
- C. Tian and Y. Liu, “Multiple positive solutions for a class of fractional singular boundary value problems,” Georgian Academy of Sciences, vol. 56, pp. 115–131, 2012.
- 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.
- 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, vol. 72, no. 2, pp. 710–719, 2010.
- Y. Liu and D. O'Regan, “Bifurcation techniques for Lidstone boundary value problems,” Nonlinear Analysis. Theory, Methods & Applications, vol. 68, no. 9, pp. 2801–2812, 2008.
- R. Ma and J. Xu, “Bifurcation from interval and positive solutions of a nonlinear fourth-order boundary value problem,” Nonlinear Analysis. Theory, Methods & Applications, vol. 72, no. 1, pp. 113–122, 2010.
- J. Xu and R. Ma, “Bifurcation from interval and positive solutions for second order periodic boundary value problems,” Applied Mathematics and Computation, vol. 216, no. 8, pp. 2463–2471, 2010.
- Y. Liu and H. Yu, “Bifurcation of positive solutions for a class of boundary value problems of fractional differential inclusions,” Abstract and Applied Analysis, vol. 2013, Article ID 942831, 8 pages, 2013.
- K. Schmitt and R. C. Thompson, Nonlinear Analysis and Differential Equations: An Introduction, University of Utah Lecture Note, Salt Lake City, Utah, USA, 2004.
- K. Schmitt, “Positive solutions of semilinear elliptic boundary value problems,” in Topological Methods in Differential Equations and Inclusions, vol. 472, pp. 447–500, Kluwer Academic Publishers, Dordrecht, The Netherlands, 1995.
- D. Guo, Nonlinear Functional Analysis, Shandong Science and Technology Press, Jinan, China, 2001, (Chinese).