RESTORE THE SOURCE FUNCTION FOR THE FRACTIONAL DIFFUSION EQUATION WITH RANDOM NOISE

Abstract

In this article we consider the problem of finding the source function of the fractional diffusion equation . Here we consider fractional derivatives in the Conformable sense. The input data is assumed to follow the Gassian white noise model. This problem is ill-posed in the Hadamard sense. Using the non-parametric estimation method and the Tikhonov regularization method, we establish the regularization solution and also estimate the error.