Existence and regularity results of a backward problem for fractional diffusion equations

In this paper, we study a backward problem for an inhomogeneous fractional diffusion equation in a bounded domain. By applying the properties of Mittag‐Leffler functions and the method of eigenvalue expansion, we establish some results about the existence, uniqueness, and regularity of the mild solutions as well as the classical solutions of the proposed problem in a weighted Hölder continuous function space.