Inverse source problem for time fractional diffusion equation with Mittag-Leffler kernel

Abstract

Abstract In this work, we study the problem to identify an unknown source term for the Atangana–Baleanu fractional derivative. In general, the problem is severely ill-posed in the sense of Hadamard. We have applied the generalized Tikhonov method to regularize the instable solution of the problem. In the theoretical result, we show the error estimate between the regularized and exact solutions with a priori parameter choice rules. We present a numerical example to illustrate the theoretical result. According to this example, we show that the proposed regularization method is converged.

Keywords

• Atangana–Baleanu derivative
• Ill-posed problem
• Time fractional diffusion equation
• Convergence estimates
• Regularization method