  The purpose of this paper is twofold. First, basic concepts such as Gamma
function, almost convergence, fractional order difference operator and sequence
spaces are given as a survey character. Thus, the current knowledge about those
concepts are presented. Second, we construct the almost convergent spaces with
fractional order difference operator and compute dual spaces which are help us
in the characterization of matrix mappings. After we characterize to the matrix
transformations, we give some examples.
