Logarithmic convexity of non‐symmetric time‐fractional diffusion equations

We consider a class of diffusion equations with the Caputo time‐fractional derivative subject to the homogeneous Dirichlet boundary conditions. Here, we consider a fractional order and a second‐order operator 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.