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In this paper, we consider the Hyers-Ulam stability for the following fractional differential equations, in the sense ofcomplex Caputo fractional derivative defined, in the unit disk: cDßzf(z)=G(f(z), cDázf(z),zf‘(z);z) 0<á<1<ß<2 . Furthermore,a generalization of the admissible functions in complex Banach spaces is imposed and applications are illustrated.