, Volume 15, Issue 2, pp 253-266
Date: 18 Mar 2012

Non-central-symmetric solution to time-fractional diffusion-wave equation in a sphere under Dirichlet boundary condition

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Abstract

The time-fractional diffusion-wave equation is considered in a sphere in the case of three spatial coordinates r, µ, and φ. The Caputo fractional derivative of the order 0 < α ≤ 2 is used. The solution is found using the Laplace transform with respect to time t, the finite Fourier transform with respect to the angular coordinate φ, the Legendre transform with respect to the spatial coordinate µ, and the finite Hankel transform of the order n + 1/2 with respect to the radial coordinate r. In the central symmetric case with one spatial coordinate r the obtained result coincides with that studied earlier. Numerical results are illustrated graphically.