LAUSR

Let $$T_n$$ T n be the class of functions $$f(z)=z+a_{n+1}z^{n+1}+a_{n+2}z^{n+2}+\ldots $$ f ( z ) = z + a n + 1 z n + 1 + a n + 2 z n + 2 + … that are analytic in the closed unit disc $$\mathbb {{\overline{U}}}.$$ U ¯ . With m different boundary points $$z_{s}, (s=1,2,\ldots , m),$$ z s , ( s = 1 , 2 , … , m ) , we consider $$\alpha _{m}\in e^{i\beta }A_{j+\lambda }f({\mathbb {U}}),$$ α m ∈ e i β A j + λ f ( U ) , here $$A_{j+\lambda }$$ A j + λ is given by using fractional derivatives $$D_{j+\lambda }f(z)$$ D j + λ f ( z ) for $$f(z)\in T_n.$$ f ( z ) ∈ T n . Using $$A_{j+\lambda },$$ A j + λ , we introduce a subclass $$P_{n}(\alpha _{m}, \beta , \rho ; j, \lambda ) $$ P n ( α m , β , ρ ; j , λ ) of $$T_n.$$ T n . The main goal of our paper is to discuss some interesting results of f ( z ) in the class $$P_{n}(\alpha _{m}, \beta , \rho ; j, \lambda ).$$ P n ( α m , β , ρ ; j , λ ) .