https://doi.org/10.1140/epjst/e2013-01972-2
Regular Article
Series expansion solutions for the multi-term time and space fractional partial differential equations in two- and three-dimensions
1 Department of Applied Mathematics, Donghua University, Shanghai 201620, PR China
2 Mathematical Sciences, Queensland University of Technology, GPO Box 2434, Brisbane, Qld. 4001, Australia
3 Department of Computing Science and OCISB, Oxford University, Oxford, OXI 3QD, UK
a e-mail: f.liu@qut.edu.au
Received: 3 June 2013
Revised: 6 August 2013
Published online: 7 October 2013
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.
© EDP Sciences, Springer-Verlag, 2013
