DETECTION OF SOURCE TERM IN AN ABSTRACT FRACTIONAL SUBDIVISION MODEL BY THE MODIFIED QUASI-BOUNDARY VALUE METHOD WITH A PRIORI AND A POSTERIORI ESTIMATE

Abstract

The paper discusses the inverse problem of determining an unknown source term in a fractional elliptic equation from measured internal data. In order to solve the considered problem, a modified quasi-boundary value method is used. Applying this method a regularized solution is constructed. An a priori and a posteriori error estimates between the exact solu- tion and its regularized approximation are obtained. A brief analysis is conducted to clarify the relationship between the suggested regularization method and several standard methods. Moreover, numerical results are presented in the one-dimensional case and two-dimensional case to illustrate the accuracy and efficiency of this method.