About this Journal Submit a Manuscript Table of Contents
The Scientific World Journal
Volume 2013 (2013), Article ID 685695, 8 pages
http://dx.doi.org/10.1155/2013/685695
Research Article

Fractional Solutions of Bessel Equation with -Method

Department of Mathematics, Firat University, 23119 Elazig, Turkey

Received 30 April 2013; Accepted 16 July 2013

Academic Editors: R. M. Guedes, Z. Mukandavire, and R. Wangkeeree

Copyright © 2013 Erdal Bas 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.

Linked References

  1. L. Adam, Fractional Calculus: History, Definitions and Applications For the Engineer, 2004.
  2. A. A. Kilbas, H. M. Srivastava, and J. J. Trujillo, Theory and Applications of Fractional Differential Equations, vol. 204 of North-Holland Mathematical Studies, Elsevier (North-Holland) Science Publishers, Amsterdam, The Netherlands, 2006.
  3. I. Podlubny, Fractional Differential Equations: An Introduction To Fractional Derivatives, Fractional Differential Equations, Methods of Their Solution and Some of Their Applications, Mathematics in Science and Enginering, vol. 198, Academic Press, New York, NY, USA, 1999.
  4. S. G. Samko, A. A. Kilbas, and O. I. Marichev, Fractional Integrals and Derivatives: Theory and Applications Translated From the Russian: Integrals and Derivatives of Fractional Order and Some of Their Applications, “Nauka i Tekhnika”, Minsk, (1987), Gordon and Breach Science Publishers, Reading, UK, 1993.
  5. K. B. Oldham and J. Spanier, The Fractional Calculus, Akademic Press, New York, NY, USA, 1974.
  6. K. Nishimoto, Fractional Calculus, vol. I, Descartes Press, Koriyama, Japan, 1984.
  7. K. Nishimoto, Fractional Calculus, vol. II, Descartes Press, Koriyama, Japan, 1987.
  8. K. Nishimoto, Fractional Calculus, vol. III, Descartes Press, Koriyama, Japan, 1989.
  9. K. Nishimoto, Fractional Calculus, vol. IV, Descartes Press, Koriyama, Japan, 1991.
  10. K. Nishimoto, Fractional Calculus, vol. V, Descartes Press, Koriyama, Japan, 1996.
  11. K. Nishimoto and S. S. de Romero, “N-fractional calculus operator Nν method to nonhomogeneous and homogeneous Whittaker Equations,” Journal of Fractional Calculus, vol. 9, pp. 17–22, 1996.
  12. K. Nishimoto, An Essence of Nishimoto’s Fractional Calculus (Calculus of the 21st Century): Integrations and Differentiations of Arbitrary Order, Descartes Press, Koriyama, Japan, 1991.
  13. M. Coz and P. Rochus, “Translation kernels for velocity dependent interactions,” Journal of Mathematical Physics, vol. 18, no. 11, pp. 2232–2240, 1976. View at Scopus
  14. A. Erdely, W. Magnus, F. Oberhettinger, and F. G. Tricomi, Tables of Integral Transform, vol. II, McGraw-Hill, New York, NY, USA, 1954.
  15. A. Erdely, “Axially symmetric potentials and fractional integration,” Journal of the Society for Industrial and Applied Mathematics, vol. 13, pp. 216–228, 1965.
  16. A. Weinstein, “Generalized axially symmetric potential theory,” Bulletin of the American Mathematical Society, vol. 59, pp. 20–38, 1953.
  17. B. Ross, Fractional Calculus and Its Applications, Conference Proceedings held at the University of New Haven, June 1974, Springer, New York, NY, USA, 1975.
  18. S. Salinas De Romero and H. M. Srivastava, “An application of the N-fractional calculus operator method to a modified Whittaker equation,” Applied Mathematics and Computation, vol. 115, no. 1, pp. 11–21, 2000. View at Scopus
  19. H. M. Srivastava and R. G. Buschman, Theory and Applications of Convolution Integral Equations, vol. 79 of Kluwer Series on Mathematics and Its Applications, Kluwer Academic Publishers, Dordrecht, The Netherlands, 1992.
  20. H. M. Srivastava, S. Owa, and K. Nishimoto, “Some fractional differintegral equations,” Journal of Mathematical Analysis and Applications, vol. 106, no. 2, pp. 360–366, 1985. View at Scopus
  21. H. Koyunbakan and E. S. Panakhov, “Transformation operator for singular Sturm-Liouville equations,” International Journal of Applied Mathematics, vol. 14, pp. 135–143, 2003.