‎A linear discrete ill-posed problem has a perturbed right-hand side vector and an ill-conditioned‎ ‎coefficient matrix‎. ‎The solution to such a problem is very sensitive to perturbation‎. ‎Replacement of the coefficient matrix by a nearby one that has less condition‎ ‎number is one of the well-known approaches for decreasing the sensitivity of the problem to perturbation. ‎In this paper‎, ‎we suggest some new regularization matrix to the Tikhonov regularization‎. ‎These new ones are based on fractional derivatives such as Grunwald-Letnikov and Caputo and can cause to have more exact solutions‎.