A comparison principle for a class of doubly nonlinear parabolic fractional partial differential equations

In this paper, we establish a comparison principle for non-negative weak solutions to a class of doubly nonlinear parabolic fractional partial differential equations within a space-time cylinder $\Omega_T=\Omega\times(0,T)\subset\mathbb{R}^{n+1}$. For the two solutions considered, we assume that at least one of them is time-independent outside the spatial domain, i.e. in $\Omega^{c}=\mathbb{R}^n\setminus\Omega$. As an application of this result, we readily infer the uniqueness of a non-negative weak solution to the corresponding Cauchy-Dirichlet problem.