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Abstract and Applied Analysis
Volume 2013 (2013), Article ID 942831, 8 pages
Bifurcation of Positive Solutions for a Class of Boundary Value Problems of Fractional Differential Inclusions
Department of Mathematics, Shandong Normal University, Jinan 250014, China
Received 11 January 2013; Revised 27 February 2013; Accepted 4 March 2013
Academic Editor: Bashir Ahmad
Copyright © 2013 Yansheng Liu and Huimin Yu. 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.
- Diethelm, The Analysis of Fractional Differential Equations: An Application-Oriented Exposition Using Differential Operators of Caputo Type, LNM 2004, Springe, 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, Mathematics in Science and Engineering, Academic Press, New York, NY, USA, 1999.
- T. Qiu and Z. Bai, “Existence of positive solutions for singular fractional diffrential equations,” Electronic Journal of Differential Equations, vol. 146, pp. 1–9, 2008.
- S. G. Samko, A. A. Kilbas, and O. I. Marichev, Fractional Integrals 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,” Memoirs on Differential Equations and Mathematical Physics, vol. 56, pp. 115–131, 2012.
- A. Boucherif and C. C. Tisdell, “Existence of periodic and non-periodic solutions to systems of boundary value problems for first-order differential inclusions with super-linear growth,” Applied Mathematics and Computation, vol. 204, no. 1, pp. 441–449, 2008.
- B. E. Paden and S. S. Sastry, “A calculus for computing Filippov's differential inclusion with application to the variable structure control of robot manipulators,” IEEE Transactions on Circuits and Systems, vol. 34, no. 1, pp. 73–82, 1987.
- L. Erbe, R. Ma, and C. C. Tisdell, “On two point boundary value problems for second order differential inclusions,” Dynamic Systems and Applications, vol. 15, no. 1, pp. 79–88, 2006.
- A. Granas and J. Dugundji, Fixed Point Theory, Springer, New York, NY, USA, 2003.
- S. Hu and N. S. Papageorgiou, Handbook of Multivalued Analysis. Vol. I, vol. 419 of Theory Mathematics and its Applications, Kluwer Academic Publishers, Dordrecht, The Netherlands, 1997.
- R. P. Agarwal, M. Benchohra, and S. Hamani, “A survey on existence results for boundary value problems of nonlinear fractional differential equations and inclusions,” Acta Applicandae Mathematicae, vol. 109, no. 3, pp. 973–1033, 2010.
- B. Ahmad and J. J. Nieto, “Sequential fractional differential equations with three-point boundary conditions,” Computers & Mathematics with Applications, vol. 64, no. 10, pp. 3046–3052, 2012.
- B. Ahmad and S. Ntouyas, “Nonlinear fractional differential equations and inclusions of arbitrary order and multi-strip boundary conditions,” Electronic Journal of Differential Equations, vol. 98, pp. 1–22, 2012.
- M. Benchohra, J. Henderson, D. Seba, et al., “Boundary value problems for fractional differential inclusions in Banach spaces,” Fractional Differential Calculus, vol. 2, pp. 99–108, 2012.
- A. Cernea, “On a multi point boundary value problem for a fractional order differential inclusion,” Arab Journal of Mathematical Sciences, vol. 19, no. 1, pp. 73–83, 2013.
- N. Nyamoradi and M. Javidi, “Existence of multiple positive solutions for fractional differential inclusion with m-point boundary conditions and two fractional orders,” Electronic Journal of Differential Equations, vol. 187, pp. 1–26, 2012.
- A. Ouahab, “Fractional semilinear differential inclusions,” Computers & Mathematics with Applications, vol. 64, no. 10, pp. 3235–3252, 2012.
- 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.
- Y. Liu and D. O'Regan, “Multiplicity results using bifurcation techniques for a class of boundary value problems of impulsive differential equations,” Communications in Nonlinear Science and Numerical Simulation, vol. 16, no. 4, pp. 1769–1775, 2011.
- 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.
- K. Deimling, Multivalued Differential Equations, Walter de Gruyter, Berlin, Germany, 1992.
- K. Schmitt and R. C. Thompson, Nonlinear Analysis and Differential Equations: An Introduction, University of Utah Lecture Note, Salt Lake City, Utah, 2004.
- K. Schmitt, “Positive Solutions of Semilinear Elliptic Boundary Value Problems,” Kluwer, Dordrecht, The Netherlands, 1995.
- D. Guo, “Eigen values and eigen vectors of nonlinear operators,” Chinese Annals of Mathematics, vol. 2, pp. 65–80, 1981.