Abstract
This paper is concerned with the dynamics and control of the fractional version of the discrete double scroll hyperchaotic map. Using phase portraits and bifurcation diagrams, we show that the general behavior of the proposed map depends on the fractional order. We also present two control schemes for the proposed map, one that adaptively stabilizes the map, and another to achieve the complete synchronization of a pair of maps. Numerical results are presented to illustrate the findings.