Analysis of a Hidden-Memory Variably Distributed-Order Time-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 (alpha) over bar (0).

Automated summary

This study analyzes the well-posedness and regularity of a variably distributed-order time-fractional diffusion equation with a hidden-memory fractional derivative, which is a competitive approach for describing the anomalous transport of particles in heterogeneous media. It is proven that the solution of such an equation exhibits weak singularity at the initial time, dependent on the upper bound of the distributed order.