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Applied Mathematics and Mechanics (English Edition) ›› 2014, Vol. 35 ›› Issue (1): 49-62.doi: https://doi.org/10.1007/s10483-014-1771-6

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

刘小靖 王记增 王晓敏 周又和   

  1. 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
  • 收稿日期:2013-04-16 修回日期:2013-08-06 出版日期:2014-01-20 发布日期:2013-12-27

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

 LIU Xiao-Jing, WANG Ji-Zeng, WANG Xiao-Min, ZHOU You-He   

  1. 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
  • Received:2013-04-16 Revised:2013-08-06 Online:2014-01-20 Published:2013-12-27

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摘要：

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.

关键词: exact solution, Laplace transform, wavelet, fractional derivative, diffusion-wave equation, integral transform

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.

Key words: null, integral transform, exact solution, diffusion-wave equation, wavelet, fractional derivative, Laplace transform

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