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Journal of Function Spaces and Applications
Volume 2013 (2013), Article ID 915830, 7 pages
http://dx.doi.org/10.1155/2013/915830
Research Article

Fundamental Spectral Theory of Fractional Singular Sturm-Liouville Operator

Department of Mathematics, Faculty of Science, Firat University, 23119 Elazig, Turkey

Received 29 May 2013; Accepted 19 July 2013

Academic Editor: Kehe Zhu

Copyright © 2013 Erdal Bas. 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.

Linked References

  1. R. S. Johnson, An Introduction To Sturm-Liouville Theory, University of Newcastle, 2006.
  2. A. Zettl, Sturm-Liouville Theory, vol. 121 of Mathematical Surveys and Monographs, American Mathematical Society, Providence, RI, USA, 2005. View at Zentralblatt MATH · View at MathSciNet
  3. W. O. Amrein, A. M. Hinz, and D. B. Pearson, Eds., Sturm-Liouville Theory, Past and Present, Birkhäuser, Basel, Switzerland, 2005. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  4. E. S. Panakhov and R. Yilmazer, “A Hochstadt-Lieberman theorem for the hydrogen atom equation,” Applied and Computational Mathematics, vol. 11, no. 1, pp. 74–80, 2012. View at MathSciNet
  5. B. M. Levitan and I. S. Sargsjan, Introduction to Spectral Theory: Self adjoint Ordinary Differential Operators, American Mathematical Society, Providence, RI, USA, 1975. View at MathSciNet
  6. J. Qi and S. Chen, “Eigenvalue problems of the model from nonlocal continuum mechanics,” Journal of Mathematical Physics, vol. 52, no. 7, Article ID 073516, 2011. View at Publisher · View at Google Scholar · View at MathSciNet
  7. E. S. Panakhov and M. Sat, “Reconstruction of potential function for Sturm-Liouville operator with Coulomb potential,” Boundary Value Problems, vol. 2013, article 49, 2013. View at Publisher · View at Google Scholar · View at MathSciNet
  8. A. Carpinteri and F. Mainardi, Eds., Fractals and Fractional Calculus in Continum Mechanics, Telos: Springer, 1998. View at MathSciNet
  9. B. J. West, M. Bologna, and P. Grigolini, Physics of Fractal Operators, Springer, New York, NY, USA, 2003. View at Publisher · View at Google Scholar · View at MathSciNet
  10. I. Podlubny, Fractional Differential Equations, vol. 198, Academic Press, San Diego, Calif, USA, 1999. View at MathSciNet
  11. R. Hilfer, Ed., Applications of Fractional Calculus in Physics, World Scientific, Singapore, 2000. View at Publisher · View at Google Scholar · View at MathSciNet
  12. S. G. Samko, A. A. Kilbas, and O. I. Marichev, Fractional Integrals and Derivatives: Theory and Applications, Gordon and Breach, Philadelphia, Pa, USA, 1993. View at MathSciNet
  13. K. S. Miller and B. Ross, An Introduction to the Fractional Calculus and Fractional Differential Equations, John Wiley & Sons, New York, NY, USA, 1993. View at MathSciNet
  14. A. A. Kilbas, H. M. Srivastava, and J. J. Trujillo, Theory and Applications of Fractional Differential Equations, vol. 204, Elsevier, Amsterdam, The Netherlands, 2006. View at MathSciNet
  15. R. Yilmazer and E. Bas, “Fractional solutions of confluent hypergeometric equation,” Journal of the Chungcheong Mathematical Society, vol. 25, no. 2, pp. 149–157, 2012.
  16. X. Jiang and H. Qi, “Thermal wave model of bioheat transfer with modified Riemann-Liouville fractional derivative,” Journal of Physics A, vol. 45, no. 48, Article ID 485101, 2012. View at Publisher · View at Google Scholar · View at MathSciNet
  17. X. Jiang and M. Xu, “The time fractional heat conduction equation in the general orthogonal curvilinear coordinate and the cylindrical coordinate systems,” Physica A, vol. 389, no. 17, pp. 3368–3374, 2010. View at Publisher · View at Google Scholar · View at MathSciNet
  18. E. Nakai and G. Sadasue, “Martingale Morrey-Campanato spaces and fractional integrals,” Journal of Function Spaces and Applications, vol. 2012, Article ID 673929, 29 pages, 2012. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  19. Y. Wang, L. Liu, and Y. Wu, “Existence and uniqueness of a positive solution to singular fractional differential equations,” Boundary Value Problems, vol. 2012, article 81, 2012. View at Publisher · View at Google Scholar · View at MathSciNet
  20. D. Băleanu and O. G. Mustafa, “On the existence interval for the initial value problem of a fractional differential equation,” Hacettepe Journal of Mathematics and Statistics, vol. 40, no. 4, pp. 581–587, 2011. View at Zentralblatt MATH · View at MathSciNet
  21. M. Klimek, On Solutions of Linear Fractional Differential Equations of a Variational Type, The Publishing Office of Czestochowa, University of Technology, Czestochowa, Poland, 2009.
  22. Q. M. Al-Mdallal, “An efficient method for solving fractional Sturm-Liouville problems,” Chaos, Solitons and Fractals, vol. 40, no. 1, pp. 183–189, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  23. V. S. Ertürk, “Computing eigenelements of Sturm-Liouville problems of fractional order via fractional differential transform method,” Mathematical & Computational Applications, vol. 16, no. 3, pp. 712–720, 2011. View at Zentralblatt MATH · View at MathSciNet
  24. M. Klimek and O. P. Argawal, “On a regular fractional Sturm-Liouville problem with derivatives of order in (0, 1),” in Proceedings of the 13th International Carpathian Control Conference, May 2012.