  There are several approaches to the fractional differential operator.
Generalized q-fractional difference operator was defined in the aid of
q-iterated Cauchy integral and q-calculus techniques. We introduce Caputo type
derivative related to this operator and some properties of this operator as
boundness are investigated. Moreover, related q-difference equation is
discussed and in the aid of q-successive approximation , existence and
uniqueness are studied.
