Regularization for a Riesz-Feller space fractional backward diffusion problem with a time-dependent coefficient

• DOI: 10.32508/stdjns.v1it5.551
• Publication Date: 2018-11-30T02:25:27Z
• Authors: Hai Nguyen Duy Dinh
• Keywords: 0101 mathematics; 01 natural sciences

In the present paper, we consider a backward problem for a space-fractional diffusion equation (SFDE) with a time-dependent coefficient. Such the problem is obtained from the classical diffusion equation by replacing the second-order spatial derivative with the Riesz-Feller derivative of order α∈(0,2]. This problem is ill-posed, i.e., the solution (if it exists) does not depend continuously on the data. Therefore, we propose one new regularization solution to solve it. Then, the convergence estimate is obtained under a priori bound assumptions for exact solution.