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

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.

arXiv commentThis is a preprint of a paper whose final and definite form is with 'Computers and Mathematics with Applications', ISSN 0898-1221. Submitted 10-Oct-2018; revised 18-May-2019; accepted for publication 25-May-2019

References in corpus (4)

• The Variable-Order Fractional Calculus of Variations
• A survey on fuzzy fractional differential and optimal control nonlocal evolution equations
• Direct transcription methods based on fractional integral approximation formulas for solving nonlinear fractional optimal control problems
• Galerkin Spectral Method for the Fractional Nonlocal Thermistor Problem

Cited by in corpus (1)

• Traveling wave solutions of some important Wick-type fractional stochastic nonlinear partial differential equations