Analytical solutions for a time-fractional axisymmetric diffusion-wave equation with a source term

作者：Zhang, Fangfang^*; Jiang, Xiaoyun

来源：Nonlinear Analysis: Real World Applications , 2011, 12(3): 1841-1849.

DOI：10.1016/j.nonrwa.2010.11.015

• Fractional diffusion-wave equation
• Caputo fractional derivative
• Integral transform
• Mittag-Leffler function

In this paper, a time-fractional axisymmetric diffusion-wave equation with a source term is considered in cylindrical coordinates. The analytical solution is obtained with the help of an integral transform method and some properties of special functions. In addition, we discuss two kinds of different boundary conditions and different forms of the source term. Finally, we analyze the effects of the fractional derivative on the solutions by using numerical results and find that sub-diffusion phenomena and oscillations exist.

• 出版日期2011-6
• 单位山东大学