Indian Journal of Industrial and Applied Mathematics
  • Year: 2020
  • Volume: 11
  • Issue: 1

Existence Results for Fractional Diffusion Equation with Dirichlet Boundary Condition

  • Author:
  • R. Saranya1,, A. Akilandeeswari2, N. Annapoorani3
  • Total Page Count: 11
  • Published Online: Oct 31, 2020
  • Page Number: 1 to 11

1Department of Applied Mathematics, Bharathiar University, Coimbatore, Tamil Nadu, India

2Department of Mathematics Bharathiar University, Coimbatore, Tamil Nadu, India. akilamathematics@gmail.com

3Department of Applied Mathematics, Bharathiar University, Coimbatore, Tamil Nadu, India. pooranimaths@gmail.com

*(Corresponding author) E-mail: *saranyarr1993@gmail.com

Online published on 31 October, 2020.

Abstract

In this article, we investigate the time-fractional diffusion equation with homogeneous Dirichlet boundary condition. The existence and uniqueness of a solution to the equation is proved using Lax-Milgram theorem. Then the time is discretized with the help of the finite difference scheme and stability result for the semi-discretized problem is shown. Furthermore, space is discretized using the idea of triangulation in the finite element method.

2010 Mathematics Subject Classifications: 35A01, 35R11.

Keywords

Fractional diffusion equation, Finite element method, Error estimates