Zhang, Xinguang; Liu, Lishan; Wiwatanapataphee, Benchawan; Wu, Yonghong Positive solutions of eigenvalue problems for a class of fractional differential equations with derivatives. (English) Zbl 1242.34015 Abstr. Appl. Anal. 2012, Article ID 512127, 16 p. (2012). Summary: By establishing a maximal principle and constructing upper and lower solutions, the existence of positive solutions for the eigenvalue problem of a class of fractional differential equations is discussed. Some sufficient conditions for the existence of positive solutions are established. Cited in 30 Documents MSC: 34A08 Fractional ordinary differential equations PDF BibTeX XML Cite \textit{X. Zhang} et al., Abstr. Appl. Anal. 2012, Article ID 512127, 16 p. (2012; Zbl 1242.34015) Full Text: DOI References: [1] I. Podlubny, Fractional Differential Equations, vol. 198 of Mathematics in Science and Engineering, Academic Press, San Diego, Calif, USA, 1999. · Zbl 1056.93542 [2] S. G. Samko, A. A. Kilbas, and O. I. Marichev, Fractional Integrals and Derivatives, Theory and Applications, Gordon and Breach, Yverdon, Switzerland, 1993. · Zbl 0924.44003 [3] K. S. Miller and B. Ross, An Introduction to the Fractional Calculus and Fractional Differential Equations, John Wiley & Sons, New York, NY, USA, 1993. · Zbl 0943.82582 [4] 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. · Zbl 1031.34002 [5] 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. · Zbl 1033.34007 [6] 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. · Zbl 1092.45003 [7] 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. · Zbl 1181.34008 [8] 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. · Zbl 1214.34007 [9] 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. · Zbl 1255.34010 [10] 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. · Zbl 1192.34008 [11] 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. · Zbl 1244.34009 [12] 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. · Zbl 1204.34007 [13] 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. · Zbl 1253.34012 [14] 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. · Zbl 1197.34003 [15] 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. · Zbl 1254.34016 [16] 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. · Zbl 1220.34006 [17] 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. · Zbl 1235.34027 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.