On Subclass of Analytic Functions Defined by q-Analogue of Modified Tremblay Fractional Derivative Operator

In this research, by using the principle of quantum calculus, we introduce a modified fractional derivative operator Tξ,q, of the analytic functions in the open unit disc =\:,||<1\. The operator Tξ,q, can then be used to introduce a new subclass of analytic functions D(ϑ,,d,ξ,γ;q). We present the necessary conditions for functions belonging to the subclass D(ϑ,,d,ξ,γ;q).\\ Furthermore, we discuss a growth and distortion bounds, the convolution condition, and the radii of starlikeness. In addition, we present neighbourhoods problems involving the q-analogue of a modified Tremblay operator for functions in the introduced class D(ϑ,,d,ξ,γ;q).