# A Finite Element Approximation for a Class of Caputo Time-Fractional Diffusion Equations

## TL;DR

This paper introduces a finite element and finite difference scheme for solving Caputo time-fractional diffusion equations, providing stability, error analysis, and numerical validation of the method's accuracy and efficiency.

## Contribution

It presents a novel fully discrete numerical scheme combining finite difference in time and finite element in space for Caputo fractional diffusion equations, with proven stability and error estimates.

## Key findings

- The method is stable under certain conditions.
- Error estimates demonstrate the scheme's accuracy.
- Numerical examples confirm efficiency and reliability.

## Abstract

We develop a fully discrete scheme for time-fractional diffusion equations by using a finite difference method in time and a finite element method in space. The fractional derivatives are used in Caputo sense. Stability and error estimates are derived. The accuracy and efficiency of the presented method is shown by conducting two numerical examples.