Exact solutions of multi-term fractional diffusion-wave equations with Robin type boundary conditions |
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Authors: | Xiao-jing Liu Ji-zeng Wang Xiao-min Wang You-he Zhou |
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Institution: | Key Laboratory of Mechanics on Disaster and Environment in Western China, Ministry of Education, School of Civil Engineering and Mechanics, Lanzhou University, Lanzhou 730000, P. R. China |
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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. |
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Keywords: | fractional derivative diffusion-wave equation Laplace transform integral transform exact solution wavelet |
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