  We consider a class of diffusion equations with the Caputo time-fractional
derivative $\partial_t^\alpha u=L u$ subject to the homogeneous Dirichlet
boundary conditions. Here, we consider a fractional order $0<\alpha < 1$ and a
second-order operator $L$ which is elliptic and non-symmetric. In this paper,
we show that the logarithmic convexity extends to this non-symmetric case
provided that the drift coefficient is given by a gradient vector field. Next,
we perform some numerical experiments to validate the theoretical results in
both symmetric and non-symmetric cases. Finally, some conclusions and open
problems will be mentioned.
