Identifying the source for Fractional diffusion equations with Random Gaussian white noise

By Ngo Ngoc Hung, Tran Thanh Binh, Nguyen Duc Phuong
DOI: 10.37550/tdmu.EJS/2023.05.426

In this work, we study the problem of finding the source function of the inhomogeneous
diffusion equations with conformable derivative c∂α
t u−Δu = f(x), 0 < α < 1, associate
with random noisy input data. This problem is ill-posed in the sense of Hadamard. In
order to regulate the instablity of the solution, we applied the truncation method and
estimated the error estimate between the exact solution and the regularized solution.