About this Journal Submit a Manuscript Table of Contents
Abstract and Applied Analysis
Volume 2014 (2014), Article ID 872318, 5 pages
http://dx.doi.org/10.1155/2014/872318
Research Article

Local Fractional Derivative Boundary Value Problems for Tricomi Equation Arising in Fractal Transonic Flow

1College of Materials Science and Engineering, Taiyuan University of Technology, Taiyuan 030024, China
2College of Mathematics and Information Science, Qujing Normal University, Qujing, Yunnan 655011, China
3Department of Electronic and Information Technology, Jiangmen Polytechnic, Jiangmen 529090, China

Received 19 June 2014; Accepted 26 June 2014; Published 13 July 2014

Academic Editor: Xiao-Jun Yang

Copyright © 2014 Xiao-Feng Niu 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. F. Tricomi, On Second-Order Linear Partial Differential Equations of Mixed Type, Leningrad, Moscow, Russia, 1947.
  2. A. R. Manwell, “The Tricomi equation with applications to the theory of plane transonic flow,” Recon Technical Report A 27617, 1979.
  3. D. Lupo and K. R. Payne, “A dual variational approach to a class of nonlocal semilinear Tricomi problems,” Nonlinear Differential Equations and Applications, vol. 6, no. 3, pp. 247–266, 1999. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  4. J. U. Kim, “An Lp a priori estimate for the Tricomi equation in the upper half space,” Transactions of the American Mathematical Society, vol. 351, no. 11, pp. 4611–4628, 1999. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  5. J. M. Rassias, “Uniqueness of quasi-regular solutions for a bi-parabolic elliptic bi-hyperbolic Tricomi problem,” Complex Variables. Theory and Application, vol. 47, no. 8, pp. 707–718, 2002. View at Publisher · View at Google Scholar · View at MathSciNet
  6. K. Yagdjian, “Global existence for the n-dimensional semilinear Tricomi-type equations,” Communications in Partial Differential Equations, vol. 31, no. 4–6, pp. 907–944, 2006. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  7. K. Yagdjian, “A note on the fundamental solution for the Tricomi-type equation in the hyperbolic domain,” Journal of Differential Equations, vol. 206, no. 1, pp. 227–252, 2004. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  8. X.-J. Yang, Advanced Local Fractional Calculus and Its Applications, World Science, New York, NY, USA, 2012.
  9. A. M. Yang, Y. Z. Zhang, and Y. Long, “The Yang-Fourier transforms to heat-conduction in a semi-infinite fractal bar,” Thermal Science, vol. 17, no. 3, pp. 707–713, 2013. View at Publisher · View at Google Scholar
  10. W. H. Su, D. Baleanu, X. J. Yang, et al., “Damped wave equation and dissipative wave equation in fractal strings within the local fractional variational iteration method,” Fixed Point Theory and Applications, vol. 2013, no. 1, pp. 1–11, 2013. View at Publisher · View at Google Scholar
  11. X. J. Yang, D. Baleanu, and J. A. T. Machado, “Mathematical aspects of Heisenberg uncertainty principle within local fractional Fourier analysis,” Boundary Value Problems, no. 1, pp. 131–146, 2013.
  12. D. Baleanu, J. A. Tenreiro Machado, C. Cattani, M. C. Baleanu, and X. Yang, “Local fractional variational iteration and decomposition methods for wave equation on Cantor sets within local fractional operators,” Abstract and Applied Analysis, vol. 2014, Article ID 535048, 6 pages, 2014. View at Publisher · View at Google Scholar · View at MathSciNet
  13. X.-J. Yang, D. Baleanu, and J. T. Machado, “Systems of Navier-Stokes equations on Cantor sets,” Mathematical Problems in Engineering, vol. 2013, Article ID 769724, 8 pages, 2013. View at Publisher · View at Google Scholar · View at MathSciNet
  14. G. Yi, “Local fractional Z transform in fractal space,” Advances in Digital Multimedia, vol. 1, no. 2, pp. 96–102, 2012.
  15. X. Yang, H. M. Srivastava, J. H. He, et al., “Cantor-type cylindrical-coordinate method for differential equations with local fractional derivatives,” Physics Letters A, vol. 377, no. 28–30, pp. 1696–1700, 2013. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  16. J.-H. He, “Asymptotic methods for solitary solutions and compactons,” Abstract and Applied Analysis, vol. 2012, Article ID 916793, 130 pages, 2012. View at Publisher · View at Google Scholar · View at MathSciNet
  17. C.-G. Zhao, A.-M. Yang, H. Jafari, and A. Haghbin, “The Yang-Laplace transform for solving the IVPs with local fractional derivative,” Abstract and Applied Analysis, vol. 2014, Article ID 386459, 5 pages, 2014. View at Publisher · View at Google Scholar
  18. Z. Y. Chen, C. Cattani, and W. P. Zhong, “Signal processing for nondifferentiable data defined on Cantor sets: a local fractional Fourier series approach,” Advances in Mathematical Physics, vol. 2014, Article ID 561434, 7 pages, 2014. View at Publisher · View at Google Scholar · View at MathSciNet
  19. A. M. Yang, Y. Z. Zhang, and X. L. Zhang, “The non-differentiable solution for local fractional Tricomi equation arising in fractal transonic flow by loca l fractional variational iteration method,” Advances in Mathematical Physics, vol. 2014, Article ID 983254, 6 pages, 2014. View at Publisher · View at Google Scholar · View at MathSciNet