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In this paper we study the Cauchy problem of the incompressible fractional Navier-Stokes equations in critical variable exponent Fourier-Besov-Morrey spacern FNs(.)p(.)h(.),q(R3)with s(.)= 4-2α-3p(.).We prove global well-posedness result with small initial data belonging to FN 4-2α-3/p(.)/p(.),h(.),q(R3).The result of this paper extends some recent work.