@Article{NM-16-181,
author = {H. M. Zhang and F. W. Liu},
title = {The Fundamental Solutions of the Space, Space-Time Riesz Fractional Partial Differential Equations with Periodic Conditions},
journal = {Numerical Mathematics, a Journal of Chinese Universities},
year = {2007},
volume = {16},
number = {2},
pages = {181--192},
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.},
issn = {},
doi = {https://doi.org/},
url = {http://global-sci.org/intro/article_detail/nm/10076.html}
}