Modified degenerate Carlitz’s q-Bernoulli polynomials and numbers with weight (α, β)

The main goal of the present paper is to construct some families of the carlitz’s q-bernoulli polyno- mials and numbers. we firstly introduce the modified carlitz’s q-bernoulli polynomials and numbers with weight (p. we then define the modified degenerate carlitz’s q-bernoulli polynomials and num- bers with weight (α, β) and obtain some recurrence relations and other identities. moreover, we derive some correlations with the modified carlitz’s q-bernoulli polynomials with weight (α, β), the modified degenerate carlitz’s q-bernoulli polynomials with weight (α, β), the stirling numbers of the first kind and second kind.