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.
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