# Initial-boundary value problems for fractional diffusion equations with time-dependent coeffcients

## TL;DR

This paper investigates initial-boundary value problems for fractional diffusion equations with time-dependent coefficients, establishing the existence and uniqueness of weak and regular solutions under zero Dirichlet boundary conditions.

## Contribution

It provides a rigorous proof of the existence and uniqueness of solutions for fractional diffusion equations with variable coefficients, extending prior work to more general settings.

## Key findings

- Proved unique existence of weak solutions.
- Established regularity results for solutions.
- Extended analysis to equations with spatial and time-dependent coefficients.

## Abstract

We discuss an initial-boundary value problem for a fractional diffusion equation with Caputo time-fractional derivative where the coefficients are dependent on spatial and time variables and the zero Dirichlet boundary condition is attached. We prove the unique existence of weak and regular solutions.