Decay of solutions to parabolic-type problem with distributed order Caputo derivative

TL;DR

This paper investigates how solutions to fractional diffusion equations with distributed order Caputo derivatives decay over time, relating decay rates to the properties of the weight function near zero.

Contribution

It establishes a connection between the behavior of the weight function near zero and the decay rate of solutions, considering time-dependent elliptic operators and integrable weight functions.

Findings

Decay rate depends on the weight function near zero

Established relation between weight function behavior and solution decay

Applicable to time-dependent elliptic operators

Abstract

We consider the decay of solution to fractional diffusion equation with the distributed order Caputo derivative. We assume that the elliptic operator is time-dependent and that the weight function contained in the definition of the distributed order Caputo derivative is just integrable. We establish the relation between behavior of weight function near zero and the decay rate of solution.