期刊名称：International Journal of Differential Equations
印刷版ISSN：1687-9643
电子版ISSN：1687-9651
出版年度：2009
卷号：2009
DOI：10.1155/2009/597292
出版社：Hindawi Publishing Corporation
摘要：Let 𝒜 be the class of analytic functions in the open unit disk 𝕌. We define Θ𝛼,𝛽∶𝒜→𝒜 by (Θ𝛼,𝛽𝑓)(𝑧)∶=Γ(2−𝛼)𝑧𝛼𝐷𝛼𝑧(Γ(2−𝛽)𝑧𝛽𝐷𝛽𝑧𝑓(𝑧)),(𝛼,𝛽≠2,3,4…), where 𝐷𝛾𝑧𝑓 is the fractional derivative of 𝑓 of order 𝛾. If 𝛼,𝛽∈[0,1], then a function 𝑓 in 𝒜 is said to be in the class SP𝛼,𝛽 if Θ𝛼,𝛽𝑓 is a parabolic starlike function. In this paper, several properties and characteristics of the class SP𝛼,𝛽 are investigated. These include subordination, characterization and inclusions, growth theorems, distortion theorems, and class-preserving operators. Furthermore, sandwich theorem related to the fractional derivative is proved.
