The European Physical Journal Special Topics

, Volume 222, Issue 8, pp 1901–1914 | Cite as

Series expansion solutions for the multi-term time and space fractional partial differential equations in two- and three-dimensions

  • H. Ye
  • F. LiuEmail author
  • I. Turner
  • V. Anh
  • K. Burrage
Regular Article


Fractional partial differential equations with more than one fractional derivative in time describe some important physical phenomena, such as the telegraph equation, the power law wave equation, or the Szabo wave equation. In this paper, we consider two- and three-dimensional multi-term time and space fractional partial differential equations. The multi-term time-fractional derivative is defined in the Caputo sense, whose order belongs to the interval (1,2],(2,3],(3,4] or (0,m], and the space-fractional derivative is referred to as the fractional Laplacian form. We derive series expansion solutions based on a spectral representation of the Laplacian operator on a bounded region. Some applications are given for the two- and three-dimensional telegraph equation, power law wave equation and Szabo wave equation.


European Physical Journal Special Topic Fractional Derivative Homogeneous Dirichlet Boundary Condition Telegraph Equation Caputo Sense 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© EDP Sciences and Springer 2013

Authors and Affiliations

  1. 1.Department of Applied MathematicsDonghua UniversityShanghaiPR China
  2. 2.Mathematical SciencesQueensland University of TechnologyBrisbaneAustralia
  3. 3.Department of Computing Science and OCISBOxford UniversityOxfordUK

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