Entropy Interpretation of Hadamard Type Fractional Operators: Fractional Cumulative Entropy

Vasily E Tarasov

doi:10.3390/e24121852

Entropy Interpretation of Hadamard Type Fractional Operators: Fractional Cumulative Entropy

Entropy (Basel). 2022 Dec 19;24(12):1852. doi: 10.3390/e24121852.

Author

Vasily E Tarasov^{1

2}

Affiliations

¹ Skobeltsyn Institute of Nuclear Physics, Lomonosov Moscow State University, Moscow 119991, Russia.
² Department of Physics, 915, Moscow Aviation Institute (National Research University), Moscow 125993, Russia.

Abstract

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.

Grants and funding

This research received no external funding.