- 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
Journal of Function Spaces and Applications
Volume 2012 (2012), Article ID 672543, 8 pages
Uniqueness of Positive Solutions for a Perturbed Fractional Differential Equation
Department of Mathematics, Business College of Shanxi University, Shanxi, Taiyuan 030031, China
Received 29 September 2012; Accepted 1 November 2012
Academic Editor: To Ma
Copyright © 2012 Chen Yang and Jieming Zhang. 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.
- K. B. Oldham and J. Spanier, The Fractional Calculus, Academic Press, New York, NY, USA, 1974.
- L. Gaul, P. Klein, and S. Kemple, “Damping description involving fractional operators,” Mechanical Systems and Signal Processing, vol. 5, no. 2, pp. 81–88, 1991.
- K. S. Miller and B. Ross, An Introduction to the Fractional Calculus and Fractional Differential Equations, Wiley, New York, NY, USA, 1993.
- S. G. Samko, A. A. Kilbas, and O. I. Marichev, Fractional Integral and Derivatives (Theory and Applications), Gordon and Breach Science, Yverdon, Switzerland, 1993.
- R. Metzler, W. Schick, H. G. Kilian, and T. F. Nonnenmacher, “Relaxation in filled polymers: a fractional calculus approach,” The Journal of Chemical Physics, vol. 103, no. 16, pp. 7180–7186, 1995.
- W. G. Glockle and T. F. Nonnenmacher, “A fractional calculus approach to self-similar protein dynamics,” Biophysical Journal, vol. 68, no. 1, pp. 46–53, 1995.
- F. Mainardi, “Some basic problems in continuum and statistical mechanics,” in Fractals and Fractional Calculus in Continuum Mechanics, C. A. Carpinteri and F. Mainardi, Eds., pp. 291–348, Springer, Wien, Austria, 1997.
- K. Diethelm and A. D. Freed, “On the solutions of nonlinear fractional order differential equations used in the mod-elling of viscoplasticity in Keil,” in Scientifice Computing in Chemical Engineering II-Computa- tional Fluid Dynamics, Reaction Engineering and Molecular Properties, pp. 217–224, Springer, Heidelberg, Germany, 1999.
- I. Podlubny, Fractional Differential Equations, Mathematics in Science and Engineering, Academic Press, New York, NY, USA, 1999.
- A. A. Kilbas, H. M. Srivastava, and J. J. Trujillo, “Theory and applications of fractional differential equations,” in North-Holland Mathematics Studies, vol. 204, Elsevier, Amsterdam, The Netherlands, 2006.
- E. M. Rabei, K. I. Nawafleh, R. S. Hijjawi, S. I. Muslih, and D. Baleanu, “The Hamilton formalism with fractional derivatives,” Journal of Mathematical Analysis and Applications, vol. 327, no. 2, pp. 891–897, 2007.
- V. Lakshmikantham, “Theory of fractional functional differential equations,” Nonlinear Analysis, Theory, Methods and Applications, vol. 69, no. 10, pp. 3337–3343, 2008.
- Y. Zhou, “Existence and uniqueness of solutions for a system of fractional differential equations,” Fractional Calculus and Applied Analysis, vol. 12, pp. 195–204, 2009.
- N. Kosmatov, “A singular boundary value problem for nonlinear differential equations of fractional order,” Journal of Applied Mathematics and Computing, vol. 29, no. 1-2, pp. 125–135, 2009.
- C. Lizama, “An operator theoretical approach to a class of fractional order differential equations,” Applied Mathematics Letters, vol. 24, no. 2, pp. 184–190, 2011.
- 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.
- E. R. Kaufmann and E. Mboumi, “Positive solutions of a boundary value problem for a nonlinear fractional differential equation,” Electronic Journal of Qualitative Theory of Differential Equations, vol. 3, no. 2008, pp. 1–11, 2008.
- C. Z. Bai, “Triple positive solutions for a boundary value problem of nonlinear fractional differential equation,” Electronic Journal of Qualitative Theory of Differential Equations, vol. 24, no. 2008, pp. 1–10, 2008.
- X. Xu, D. Jiang, and C. Yuan, “Multiple positive solutions for the boundary value problem of a nonlinear fractional differential equation,” Nonlinear Analysis, Theory, Methods and Applications, vol. 71, no. 10, pp. 4676–4688, 2009.
- J. Caballero Mena, J. Harjani, and K. Sadarangani, “Existence and uniqueness of positive and nondecreasing solutions for a class of singular fractional boundary value problems,” Boundary Value Problems, vol. 2009, Article ID 421310, 10 pages, 2009.
- S. Q. Zhang, “Positive solutions to singular boundary value problem for nonlinear fractional differential equation,” Computers and Mathematics with Applications, vol. 59, no. 3, pp. 1300–1309, 2010.
- L. Yang and H. Chen, “Unique positive solutions for fractional differential equation boundary value problems,” Applied Mathematics Letters, vol. 23, no. 9, pp. 1095–1098, 2010.
- Y. Q. Wang, L. .S Liu, and Y. H. Wu, “Positive solutions for a nonlocal fractional differential equation,” Nonlinear Analysis, Theory, Methods and Applications, vol. 74, no. 11, pp. 3599–3605, 2011.
- M. El-Shahed, “Positive solutions for boundary value problems of nonlinear fractional differential equation,” Abstract and Applied Analysis, vol. 2007, Article ID 10368, 8 pages, 2007.
- S. .H Liang and J. H. Zhang, “Existence and uniqueness of strictly nondecreasing and positive solution for a fractional three-point boundary value problem,” Computers and Mathematics with Applications, vol. 62, no. 3, pp. 1333–1340, 2011.
- Y. G. Zhao, S. R. Sun, Z. L. Han, and Q. P. Li, “The existence of multiple positive solutions for boundary value problems of nonlinear fractional differential equations,” Communications in Nonlinear Science and Numerical Simulation, vol. 16, no. 4, pp. 2086–2097, 2011.
- D. Guo and V. Lakshmikantham, Nonlinear Problems in Abstract Cones, Academic Press, Boston, Mass, USA, 1988.
- C. B. Zhai, C. Yang, and X. Q. Zhang, “Positive solutions for nonlinear operator equations and several classes of applications,” Mathematische Zeitschrift, vol. 266, no. 1, pp. 43–63, 2010.