In this article, by making use of a linear multiplier fractional differential operator $D^{delta,m}_{lambda}$, we introduce a new subclass of spiral-like functions. The main object is to provide some subordination results for functions in this class. We also find sufficient conditions for a function to be in the class and derive Fekete-Szego inequalities.

Keywords: Analytic functions, $alpha$-spirallike functions of order $eta$, Fractional differential operator, Fekete-Szego problem, Subordination