Summary: We introduce two new subclasses \({\mathcal V}_\delta (p;\mu)\) and \({\mathcal W}_\delta (p;\mu)\) of analytic and \(p\)-valent functions, defined by using the fractional calculus operators (fractional derivatives). We obtain a sufficient condition for a function to belong to each of these subclasses and investigate the characteristics of functions in these subclasses. Geometric properties of multivalent functions \((p\)-valently close-to-convex, \(p\)-valently starlike and \(p\)-valently convex functions) are also considered.