Volume 16, Issue 2
The Fundamental Solutions of the Space, Space-Time Riesz Fractional Partial Differential Equations with Periodic Conditions

H. M. Zhang and F. W. Liu

Numer. Math. J. Chinese Univ. (English Ser.)(English Ser.) 16 (2007), pp. 181-192

Preview Full PDF BiBTex 26 393
  • Abstract

In this paper, the space-time Riesz fractional partial differential equations with periodic conditions are considered. The equations are obtained from the integral partial differential equation by replacing the time derivative with a Caputo fractional derivative and the space derivative with Riesz potential. The fundamental solutions of the space Riesz fractional partial differential equation (SRFPDE) and the space-time Riesz fractional partial differential equation (STRFPDE) are discussed, respectively. Using methods of Fourier series expansion and Laplace transform, we derive the explicit expressions of the fundamental solutions for the SRFPDE and the STRFPDE, respectively.

  • History

Published online: 2007-05

  • Keywords

  • AMS Subject Headings

  • Cited by