A modified quasi-boundary value method for a backward problem for the inhomogeneous time conformable fractional heat equation in a cylinder

The time conformable heat equation is a generalization of classical heat equation involved local and limit-based derivative, which is called conformable fractional derivative. In this paper, we study a backward problem for the time conformable fractional heat equation defined in cylindrical coordinates for the axis-symmetric case which is a severely ill-posed problem. By using a modified quasi-boundary value method, the problem is regularized and some new error estimates are obtained. The numerical experiment shows that the method is feasible and effective.