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

H. M. Zhang & F. W. Liu

DOI:

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

Published online: 2007-05

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  • 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.

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@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} }
TY - JOUR T1 - The Fundamental Solutions of the Space, Space-Time Riesz Fractional Partial Differential Equations with Periodic Conditions AU - H. M. Zhang & F. W. Liu JO - Numerical Mathematics, a Journal of Chinese Universities VL - 2 SP - 181 EP - 192 PY - 2007 DA - 2007/05 SN - 16 DO - http://dor.org/ UR - https://global-sci.org/intro/article_detail/nm/10076.html KW - AB - 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.
H. M. Zhang & F. W. Liu. (1970). The Fundamental Solutions of the Space, Space-Time Riesz Fractional Partial Differential Equations with Periodic Conditions. Numerical Mathematics, a Journal of Chinese Universities. 16 (2). 181-192. doi:
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