Regularization For A Fractional Sideways Heat Equation

We consider a sideways problem for a fractional heat equation. In recent years, the sideways problems have become one of the most important branches in the filed of applied mathematics and enormously promoted the development of science and en-gineering filed. Sideways problems are usually ill-posed and small change in the given measurements may result in an enormous deviation of the solution. The solution does not depend continuously on the given measurements. It is an important research subject to solve the ill-posed problem.Fractional heat equation problems have been widely applied in various areas of engineering and sciences. we investigate a sideways problem for the fractional diffusion equation in a semi-unbounded domain. The boundary data can only be measured on a portion of the boundary. This leads to an ill-posed problem of the fractional heat equation. We proposed a new regularization to solve the problem, which we call the dynamic spectral regularization method. To demonstrate the efficiency and stability of the proposed method, we provide some theoretical analysis and numerical results of the proposed method.