Simple Adaptive Control (SAC) were known to be robust against a class of disturbances and globally stable if the controlled plant is almost strictly positive real (ASPR). However, in some applications the SAC technique may still present a design complexity issue arising from the large number of parameters and coefficients to select. This design complexity has been mitigated by the recently proposed Decentralized Simple Adaptive Control (DSAC). There are still some exceptional remedies on how to improve tracking performance (flexibility, and accuracy). Fortunately, as numerous previous studies show, the introduction of fractional order calculus can considerably improve the performance of conventional and adaptive controllers. In this paper, we considerably improve the flexibility and the tracking performance of DSAC by utilizing a fractional order adaptation rule. Firstly, we try to establish the ASPR conditions for the design of a stable fractional adaptive system. We provide a fractional Order parallel feedforward compensator (FOPFC) to realize an augmented ASPR system. Then we propose the ASPR-based FODSAC controller. The stability analysis of the proposed control scheme is presented and simulation example comparing the standard DSAC with the new FODSAC is provided, showing the performance of the proposed approach.