Analysis of a Hidden Memory Variably Distributed-Order Space-Fractional Diffusion Equation

We analyze the well-posedness and regularity of a variably distributed-order time-fractional diffusion equation (tFDE) with a hidden-memory fractional derivative, which provide a competitive means to describe the anomalously diffusive transport of particles in heterogeneous media. We prove that the solution of a variably distributed-order tFDE has weak singularity at the initial time t=0 which depends on the upper bound of a distributed order α¯(0).