Some regularization methods for a class of nonlinear fractional evolution equations

Abstract

In this paper, we study initial value problems for nonlinear fractional elliptic equations. In general, the problem is not well-posed, and herein the Hadamard-instability occurs. Under some weak a priori assumptions on the sought solution, we propose two new regularization methods to stabilize the problem when the source term is a globally or locally Lipschitz function. Furthermore, we also investigate the error estimate and show that the approximate solution converges to the exact solution in L2 and H2 norms.