A $q$-Caputo Fractional Generalization of Tsallis Entropy: Series Representation and Non-Negativity Domains (opens in new tab)

arXiv:2603.23254v1 Announce Type: new Abstract: We introduce a fractional generalization of Tsallis entropy by acting with a $q$-Caputo operator on the generating family $\sum_i p_i^{\,x}$ evaluated at $x=1$. Concretely, we define $S_{q}^{\alpha}$ through the $q$-Caputo differintegral of order $0<\alpha<1$ and derive a closed series representation in terms of the $q$-Gamma function. The construction is anchored at the evaluation point, which ensures well-behaved limits: as $\alpha\!\to\!1$ w...