# Fractional diffusion equation with the distributed order Caputo derivative

## TL;DR

This paper studies a fractional diffusion equation involving a distributed order Caputo derivative, proving the existence of weak and regular solutions under minimal assumptions on the weight function.

## Contribution

It establishes the existence of solutions for a fractional diffusion equation with distributed order derivatives under broad conditions, extending previous results.

## Key findings

- Existence of weak solutions proven.
- Existence of regular solutions established.
- Results hold for general elliptic operators with integrable weight functions.

## Abstract

We consider fractional diffusion equation with the distributed order Caputo derivative. We prove existence of a weak and regular solution for general uniformly elliptic operator under the assumption that the weight function is only integrable.