We introduce some new subclasses of analytic functions which are univalent in an open unit disk by means of fractional calculus. The elemental interest is to explore the significance of fractional-order operators while formulating a few distinct subclasses of univalent analytic functions. Present work establishes the Fekete-Szegö inequality for the proposed subclasses. In addition, some classical Fekete-Szegö problems have also been retrieved and discussed as particular cases of the presented work. To make the suggested work more evident, an extremal function is also provided for which a sharp upper bound is attained.

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