Monotone method for initial value problem for fractional diffusion equation (Q867780)

The author considers the Cauchy problem for the fractional diffusion equation of the form \[ D^\alpha_t u-d^2\Delta u+c(x)u=f(t,x,u),\quad 0<t\leq T,x\in \mathbb R^n, \] where \(D^\alpha\) (\(0<\alpha <1\)) is the Caputo-Dzhrbashyan fractional derivative. The method of upper and lower solutions is used to obtain an existence and uniqueness result.