Abstract:Generalized multi-term time-fractional diffusion equations have been used to describe important physical phenomena. However, studies on multi-term time-fractional diffusion equations with mixed boundary conditions in high dimensional conditions are still limited. In this paper,a method of separating variables was effectively implemented to solve a generalized multi-term time-fractional diffusion equation (GMTDE) in a finite domain.In this equation, the multi-term time-fractional derivatives were defined in the Caputo sense, whose orders belonged to the intervals [0,1], [1,2], respectively. The space partial derivatives were classical integer order derivatives whose order were 2. We discussed and derived the analytical solution of the GMTDE in two dimensions meeting nonhomogeneous mixed boundary conditions.The technique reported can be applied to other kinds of fractional differential equations with different boundary conditions.
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