  Accelerators with power-law memory are proposed in the framework of the
discrete time approach. To describe discrete accelerators we use the capital
stock adjustment principle, which has been suggested by Matthews.The suggested
discrete accelerators with memory describe the economic processes with the
power-law memory and the periodic sharp splashes (kicks). In continuous time
approach the memory is described by fractional-order differential equations. In
discrete time approach the accelerators with memory are described by discrete
maps with memory, which are derived from the fractional-order differential
equation without approximations. In order to derive these maps we use the
equivalence of fractional-order differential equations and the Volterra
integral equations.
