Interpretations of Hadamard-type fractional integral and differential operators are proposed. The Hadamard-type fractional integrals of function with respect to another function are interpreted as an generalization of standard entropy, fractional entropies and cumulative entropies. A family of fractional cumulative entropies is proposed by using the Hadamard-type fractional operators.
Keywords: Hadamard-type fractional pperator; cummulative entropy; entropy; fractional calculus; fractional entropy; fractional integrals.