The conditional stability and an iterative regularization method for a fractional inverse elliptic problem of Tricomi-Gellerstedt-Keldysh type

Abstract

The present paper is devoted to identifying an inaccessible boundary condition for a fractional elliptic problem of Tricomi-Gellerstedt-Keldysh-type. Using the expansion Fourier method, the considered problem can be reformulated as an operator equation of the first kind. To construct a stabilized approximate solution we employ a variant of the iterative method. We also present error estimates between the exact solution and the regularized solution by the a priori and the a posteriori parameter choice rules. Finally, some numerical verifications on the efficiency and accuracy of the proposed algorithm is presented.

Keywords

• fractional elliptic equations
• Tricomi-Gellerstedt-Keldysh equations
• ill-posed problems
• inverse problems
• a posteriori parameter choice rule
• iterative regularization method