Table of Contents Author Guidelines Submit a Manuscript
Mathematical Problems in Engineering
Volume 2010, Article ID 497676, 12 pages
Research Article

On the Operator Related to Bessel Heat Equation

Department of Mathematics, Faculty of Science, Maejo University, Chiang Mai 50290, Thailand

Received 12 April 2010; Accepted 27 June 2010

Academic Editor: Carlo Cattani

Copyright © 2010 Wanchak Satsanit. 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. F. John, Partial Differential Equations, vol. 1 of Applied Mathematical Sciences, Springer, New York, NY, USA, 4th edition, 1982. View at Zentralblatt MATH · View at MathSciNet
  2. B. M. Levitan, “Expansion in Fourier series and integrals with Bessel functions,” Uspekhi Matematicheskikh Nauk, vol. 62, no. (42), pp. 102–143, 1951 (Russian). View at Google Scholar · View at MathSciNet
  3. H. Yildirim, M. Z. Sarikaya, and S. Öztürk, “The solutions of the n-dimensional Bessel diamond operator and the Fourier-Bessel transform of their convolution,” Proceedings of the Indian Academy of Sciences, vol. 114, no. 4, pp. 375–387, 2004. View at Publisher · View at Google Scholar · View at MathSciNet
  4. W. Satsanit and A. Kananthai, “On the Green function and nonlinear of Bessel Bk,” Journal of Advanced Research in Differential Equation, vol. 2, no. 1, pp. 10–29, 2010. View at Google Scholar
  5. H. Yildirim, Riesz potentials generated by a generalized shift operator, Ph.D. thesis, Ankara University, Ankara, Turkey, 1995.
  6. I. A. Kipriyanov, “Boundary value problems for partial differential equations with Bessel's differential operator,” Doklady Akademii Nauk SSSR, vol. 158, no. 2, pp. 274–278, 1964. View at Google Scholar
  7. I. A. Kipriyanov, “Fourier-Bessel transforms and imbedding theorems for weight classes,” Trudy Matematicheskogo Instituta imeni V. A. Steklova, vol. 89, pp. 130–213, 1967. View at Google Scholar
  8. A. Saglam, H. Yildirim, and M. Z. Sarikaya, “On the bessel heat equation related to the bessel diamond operator,” Acta Applicandae Mathematicae, vol. 109, no. 3, pp. 849–860, 2010. View at Publisher · View at Google Scholar · View at Scopus
  9. M. Z. Sarikaya, “On the heat equation defined by iterated continuous,” Dynamics of Continuous, Discrete and Impulsive Systems Series A. In press.