A certain subclass of analytic functions involving operators of fractional calculus

Some results concerning the Tremblay operator and some of its applications to certain analytic functions

“…Within this context and also in this present investigation, some new definitions and also applications of an operator, which is related to fractional calculus and known as the Tremblay operator in the literature, will be considered for certain functions with complex variable. For certain results relating to the Tremblay operator and also fractional calculus, one may check the paper in [1]- [3], [5], [7], [9]- [11], [15] and [16] in the references.…”

“…and also defined as in (cf., e.g., [1]- [3], [9]- [11], [14] and [15]): Let κ(z) be an analytic function in a simply-connected region of the z−plane containing the origin. Then, the fractional derivative of order µ is defined by…”

“…which was defined in the domain of the complex plane and whose properties in several spaces were discussed systematically. For instance, one may refer to the works given by [5], [9]- [3] and [14]- [16].…”

A Few Complex Equations Constituted by an Operator Consisting of Fractional Calculus and Their Consequences

“…Also let N 0 := N∪{0}, C * := C−{0}, and R * := R−{0}. For 0 ≤ < 1 and an analytic function := ( ), the symbol D [ ] denotes an operator of FC, which is defined as follows (cf., e.g., [9,[30][31][32][33]). …”

Inclusion and neighborhood properties of a certain subclasses of p-valent functions with negative coefficients

“…Several other interesting subclasses of the class T p (n) were investigated recently, for example, by Chen et al [8], Chen [7], Srivastava and Aouf [16], Murugusundarmoorthy et al [12], Altinatas [1], and Altinatas et al ([3] and [4]), (see also Srivastava and Owa [17]). …”