Inverse Source Problem for Sobolev Equation with Fractional Laplacian

Abstract

In this paper, we are interested in the problem of determining the source function for the Sobolev equation with fractional Laplacian. This problem is ill-posed in the sense of Hadamard. In order to edit the instability instability of the solution, we applied the fractional Landweber method. In the theoretical analysis results, we show the error estimate between the exact solution and the regularized solution by using an a priori regularization parameter choice rule and an a posteriori regularization parameter choice rule. Finally, we investigate the convergence of the source function when fractional order $\beta ⟶1^{+}$ .