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Abstract and Applied Analysis
Volume 2013 (2013), Article ID 789836, 7 pages
Positive Solutions of Fractional Differential Equation with -Laplacian Operator
College of Business Administration, Hunan University, Changsha, Hunan 410082, China
Received 27 November 2012; Accepted 5 February 2013
Academic Editor: Fuding Xie
Copyright © 2013 Teng Ren and Xiaochun Chen. 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.
- C. Almeida and J. Vicente, “Are interest rate options important for the assessment of interest rate risk?” Journal of Banking & Finance, vol. 33, pp. 1376–1387, 2009.
- X. Zhang and L. Liu, “Positive solutions of fourth-order four-point boundary value problems with p-Laplacian operator,” Journal of Mathematical Analysis and Applications, vol. 336, no. 2, pp. 1414–1423, 2007.
- J. Wang, H. Xiang, and Z. Liu, “Upper and lower solutions method for a class of singular fractional boundary value problems with p-Laplacian operator,” Abstract and Applied Analysis, vol. 2010, Article ID 971824, 12 pages, 2010.
- D.-X. Ma and X.-Z. Yang, “Upper and lower solution method for fourth-order four-point boundary value problems,” Journal of Computational and Applied Mathematics, vol. 223, no. 2, pp. 543–551, 2009.
- S. Chen, W. Ni, and C. Wang, “Positive solution of fourth order ordinary differential equation with four-point boundary conditions,” Applied Mathematics Letters, vol. 19, no. 2, pp. 161–168, 2006.
- Z. Bai and H. Lv, “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.
- K. S. Miller and B. Ross, Introduction to the Fractional Calculus and Fractional Differential Equations, Wiley, New York, NY, USA, 1993.
- M. Jia, X. Liu, and X. Gu, “Uniqueness and asymptotic behavior of positive solutions for a fractional-order integral boundary value problem,” Abstract and Applied Analysis, vol. 2012, Article ID 294694, 21 pages, 2012.
- M. Jia, X. Zhang, and X. Gu, “Nontrivial solutions for a higher fractional differential equation with fractional multi-point boundary conditions,” Boundary Value Problems, vol. 2012, article 70, 2012.
- 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.
- 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.
- X. Zhang, L. Liu, and Y. Wu, “The uniqueness of positive solution for a singular fractional differential system involving derivatives,” Communications in Nonlinear Science and Numerical Simulation, vol. 18, pp. 1400–1409, 2013.
- X. Zhang, L. Liu, B. Wiwatanapataphee, and Y. Wu, “Positive solutions of eigenvalue problems for a class of fractional differential equations with derivatives,” Abstract and Applied Analysis, vol. 2012, Article ID 512127, 16 pages, 2012.
- X. Zhang, L. Liu, and Y. Wu, “Existence results formultiple positive solutions of nonlinear higher order perturbed fractional differential equations with derivatives,” Applied Mathematics and Computation, vol. 219, no. 4, pp. 1420–1433, 2012.
- X. Zhang, L. Liu, Y. Wu, and Y. Lu, “The iterative solutions of nonlinear fractional differential equations,” Applied Mathematics and Computation, vol. 219, no. 9, pp. 4680–4691, 2013.
- I. Podlubny, Fractional Differential Equations, Mathematics in Science and Engineering, Academic Press, New York, NY, USA, 1999.
- S. G. Samko, A. A. Kilbas, and O. I. Marichev, Fractional Integrals and Derivatives, Gordon and Breach Science, Yverdon, Switzerland, 1993.