International Science and Technology Journal

Two new fractional entropy functions, first, based on extension of Ubriaco and Shafee approach, and second, the generalization through the use of concept of expansion of linear fractional distributed order derivative, is proposed. The first entropies are the two-parametric functions. The second entropy is a linear combination of the above functions. Then they have the same properties as the Shannon entropy except additivity. For q1, q2 (0,1], these entropies satisfy the third law of thermodynamics in the Bento sense, and, for q1 ≤ 1 and q2 ≥ 1, the Lesche stability criteria.