An Extension to the Owa-Srivastava Fractional Operator with Applications to Parabolic Starlike and Uniformly Convex Functions. (18th January 2009)

• Record Type: Journal Article
• Authors: Al-Refai, Oqlah; Darus, Maslina
• Other Names: Momani Shaher Academic Editor.
• Is Part Of: International journal of differential equations. Volume 2009(2009)
• Publication Date: 2009-01-18
• Subjects: Differential equations -- Periodicals; Differential equations; Periodicals; 515.35
• DOI: 10.1155/2009/597292
• Languages: English
• ISSNs: 1687-9643

Abstract

Abstract : Let𝒜 be the class of analytic functions in the open unit disk 𝕌. We defineΘ α, β : 𝒜 → 𝒜 by( Θ α, β f ) ( z ) : = Γ ( 2 − α ) z α D z α ( Γ ( 2 − β ) z β D z β f ( z ) ), ( α, β ≠ 2, 3, 4 … ), whereD z γ f is the fractional derivative off of orderγ . Ifα, β ∈ [ 0, 1 ], then a functionf in𝒜 is said to be in the classS P α, β ifΘ α, β f is a parabolic starlike function. In this paper, several properties and characteristics of the classS P α, 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.