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Abstract and Applied Analysis
Volume 2013 (2013), Article ID 615707, 6 pages
Unique Solution of a Coupled Fractional Differential System Involving Integral Boundary Conditions from Economic Model
1Department of Electrical Engineering, North China Electric Power University, Baoding 071003, China
2Department of Management and Economic, North China Electric Power University, Baoding 071003, China
3School of Land Science and Technology, China University of Geosciences, Beijing 100083, China
4Institute of Finance and Banking, Chinese Academy of Social Sciences, Beijing, China
Received 13 May 2013; Accepted 1 July 2013
Academic Editor: Yonghong Wu
Copyright © 2013 Rui Li 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.
- J. R. L. Webb and G. Infante, “Positive solutions of nonlocal boundary value problems involving integral conditions,” Nonlinear Differential Equations and Applications, vol. 15, no. 1-2, pp. 45–67, 2008.
- J. R. L. Webb and G. Infante, “Positive solutions of nonlocal boundary value problems: a unified approach,” Journal of the London Mathematical Society, vol. 74, no. 3, pp. 673–693, 2006.
- J. R. L. Webb, “Nonlocal conjugate type boundary value problems of higher order,” Nonlinear Analysis. Theory, Methods & Applications A, vol. 71, no. 5-6, pp. 1933–1940, 2009.
- X. Hao, L. Liu, Y. Wu, and Q. Sun, “Positive solutions for nonlinear nth-order singular eigenvalue problem with nonlocal conditions,” Nonlinear Analysis. Theory, Methods & Applications A, vol. 73, no. 6, pp. 1653–1662, 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.
- H. Tao, M. Fu, and R. Qian, “Positive solutions for fractional differential equations from real estate asset securitization via new fixed point theorem,” Abstract and Applied Analysis, vol. 2012, Article ID 842358, 11 pages, 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, 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.
- 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.
- W. Wang and L. Huang, “Existence of positive solution for semipositone fractional differential equations involving Riemann-Stieltjes integral conditions,” Abstract and Applied Analysis, vol. 2012, Article ID 723507, 17 pages, 2012.
- X. Zhang, L. Liu, and Y. Wu, “Existence results for multiple 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.
- 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.
- 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.
- J. Harjani and K. Sadarangani, “Fixed point theorems for weakly contractive mappings in partially ordered sets,” Nonlinear Analysis. Theory, Methods & Applications A, vol. 71, no. 7-8, pp. 3403–3410, 2009.
- K. S. Miller and B. Ross, An Introduction to the Fractional Calculus and Fractional Differential Equations, John Wiley & Sons, New York, NY, USA, 1993.
- I. Podlubny, Fractional Differential Equations, Mathematics in Science and Engineering, vol. 198, Academic Press, San Diego, Calif, USA, 1999.
- A. A. Kilbas, H. M. Srivastava, and J. J. Trujillo, Theory and Applications of Fractional Differential Equations, vol. 204, Elsevier, Amsterdam, The Netherlands, 2006.
- 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.
- 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.
- J. Caballero, J. Harjani, and K. Sadarangani, “On existence and uniqueness of positive solutions to a class of fractional boundary value problems,” Boundary Value Problems, vol. 2011, 25 pages, 2011.