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In this paper, we define a new subclass of -uniformly starlike functions of order by using certain generalized -integral operator. We explore geometric interpretation of the functions in this class by connecting it with conic domains. We also investigate -sufficient coefficient condition, -Fekete-Szeg\"{o} inequalities, -Bieberbach-De Branges type coefficient estimates and radius problem for functions in this class. We conclude this paper by introducing an analogous subclass of -uniformly convex functions of order by using the generalized -integral operator. We omit the results for this new class because they can be directly translated from the corresponding results of our main class.