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In this brief, the designs of fixed-fractional-delay FIR filters using fractional-derivative constraints are presented. There are two kinds of designs to be studied. One is the least squares design in which the filter coefficients are determined by minimizing integral square error under the constraint that the ideal response and actual response have several same fractional derivatives at the prescribed frequency point. The other is the maximally flat design in which the filter coefficients are determined by letting the number of fractional-derivative constraints be equal to the number of filter coefficients. Numerical examples are demonstrated to show that the proposed method has larger design flexibility than the conventional integer derivative constrained methods.