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Exact solutions of multi-term fractional diffusion-wave equations with Robin type boundary conditions

Research paper by Xiao-jing Liu, Ji-zeng Wang, Xiao-min Wang, You-he Zhou

Indexed on: 13 Dec '13Published on: 13 Dec '13Published in: Applied Mathematics and Mechanics



Abstract

General exact solutions in terms of wavelet expansion are obtained for multiterm time-fractional diffusion-wave equations with Robin type boundary conditions. By proposing a new method of integral transform for solving boundary value problems, such fractional partial differential equations are converted into time-fractional ordinary differential equations, which are further reduced to algebraic equations by using the Laplace transform. Then, with a wavelet-based exact formula of Laplace inversion, the resulting exact solutions in the Laplace transform domain are reversed to the time-space domain. Three examples of wave-diffusion problems are given to validate the proposed analytical method.