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Discrete models of dislocations in fractional nonlocal materials are suggested. The proposed models are based on fractional-order differences instead of finite differences of integer orders that are usually used. The fractional differences allow us to describe long-range interactions in materials. In continuous limit the suggested discrete models give continuum models of dislocations in nonlocal continua. Fractional generalization of the Frenkel-Kontorova model by using long-range interactionsdoi:10.1016/j.jksus.2015.04.001 fatcat:t72xhrhrgnakhgxx3wqp5pcsm4