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Recently considerable effort has been devoted to the study of fractional calculus in many branches of mathematics and physics. The main object of the present investigation is to provide a brief survey concerning fractional integral and derivative operators in Geometric Function Theory. The generalizations of these operators are also concerned along with numerous properties of these generalized operators. We also list some samples which reflect our recent investigations in the Geometric Function Theory. [ABSTRACT FROM AUTHOR]

Using the q-derivative operator in conjunction with the principle of subordination between analytic functions, we introduce two subclasses of analytic functions in the open unit disk U. We investigate convolution properties and coefficient estimates for these subclasses. [ABSTRACT FROM AUTHOR]

In the literature on geometric function theory, we can find many interesting applications of a variety of convolution operators which are defined by means of a number of special functions and analytic number theory. The main object of this paper is to examine two subclasses of multivalent functions of the form which are analytic in the open unit disc U. We investigate convolution properties and coefficient estimates for these subclasses. [ABSTRACT FROM AUTHOR]

In this paper, we obtain Fekete-Szegö functional ∣ap+2 - μa2p+1∣ for functions of the class Mm,λb,p,q(g, φ). Sharp bounds for the Fekete-Szegö functional ∣ap+2 - μa2p+1∣ are obtained. [ABSTRACT FROM AUTHOR]

Using of the principle of subordination, we investigate some subordination and convolution properties for classes of multivalent functions under certain assumptions on the parameters involved, which are defined by a generalized fractional differintegral operator under certain assumptions on the parameters involved. [ABSTRACT FROM AUTHOR]