On the friable mean value of additive arithmetic functions

Using the Turán–Kubilius inequality for y-friable integers proved by De la Brèteche and Tenenbaum. We provide, the friable mean value of the additive function f where f(n) is either $$ \tilde{\omega }(n)$$ or $$\tilde{\Omega }(n),$$ the number of distinct prime factors, the total number of prime factors p of a positive integer n such that $$s_q(p)\equiv a (\mathrm{mod\,}b) $$ $$(a,b\in {\mathbb {Z}}, b\geqslant 2)$$ and $$s_q(n)$$ denote the sum of the digits in base $$q\geqslant 2$$ of the positive integer n.