On the second realization for the positive part of $$U_q(\widehat{sl_2})$$ of equitable type

The equitable presentation of the quantum algebra $U_q(\widehat{sl_2})$ is considered. This was originally introduced by T. Ito and P. Terwilliger. In this paper, following Terwilliger's recent works (nonstandard) positive part type $U_q^{IT,+}$ its second realization (current algebra) $U_q^{T,+}$ are studied. A for given in terms a K-operator satisfying Freidel-Maillet equation condition on determinant. Realizations Ding-Frenkel L-operators considered, from which an explicit injective homomorphism to subalgebra Drinfeld's derived, comodule structure characterized. central extension relation with $U_q(\widehat{gl_2})$ also described using framework algebras.