LAUSR

In this work, we are interested to study the initial inverse problem for elliptic equation with Caputo derivative. We obtained some different results regarding the well-posedness of the solution corre-sponding to the given input data. In addition, we also derive the upper bound of the derivative of the mild solution. The principal analysis is based on the estimation of the Mittag-Leffler function, combined with main analysis in Hilbert scale authorized, and we also use fixed point techniques to prove the inequalities in this paper.