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In this paper, a generalized multivariate fractional Taylor's and Cauchy's mean value theorem of the kind f(x,y) = _j = 0^n D^jα f(x_0, y_0) Γ (jα + 1) + R_n^α (ξ,η),f(x,y) - _j = 0^n D^jα f(x_0, y_0) Γ (jα + 1) g(x,y) - _j = 0^n D^jα g(x_0, y_0) Γ (jα + 1) = R_n^α (ξ ,η ) T_n^α (ξ ,η ) , where 0, number=1, journal=Journal of Mathematical Study, year=2019, month=Mar., pages=38–52