An Extension to the Owa-Srivastava Fractional Operator with Applications to Parabolic Starlike and Uniformly Convex Functions
Let 𝒜 be the class of analytic functions in the open unit disk . We define Θα,β:𝒜→𝒜 by (Θα,βf)(z):=Γ(2−α)zαDzα(Γ(2−β)zβDzβf(z)),(α,β≠2,3,4…), where Dzγf 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...
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Wiley
2009-01-01
|
| Series: | International Journal of Differential Equations |
| Online Access: | http://dx.doi.org/10.1155/2009/597292 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1832556310763143168 |
|---|---|
| author | Oqlah Al-Refai Maslina Darus |
| author_facet | Oqlah Al-Refai Maslina Darus |
| author_sort | Oqlah Al-Refai |
| collection | DOAJ |
| description | Let 𝒜 be the class of analytic functions in the open unit disk . We define Θα,β:𝒜→𝒜 by (Θα,βf)(z):=Γ(2−α)zαDzα(Γ(2−β)zβDzβf(z)),(α,β≠2,3,4…), where Dzγf 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. |
| format | Article |
| id | doaj-art-0ab2d9b227674f5a90ec6e483905c102 |
| institution | Kabale University |
| issn | 1687-9643 1687-9651 |
| language | English |
| publishDate | 2009-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Differential Equations |
| spelling | doaj-art-0ab2d9b227674f5a90ec6e483905c1022025-02-03T05:45:42ZengWileyInternational Journal of Differential Equations1687-96431687-96512009-01-01200910.1155/2009/597292597292An Extension to the Owa-Srivastava Fractional Operator with Applications to Parabolic Starlike and Uniformly Convex FunctionsOqlah Al-Refai0Maslina Darus1School of Mathematical Sciences, Faculty of Science and Technology, University Kebangsaan Malaysia, Bangi 43600, Selangor, MalaysiaSchool of Mathematical Sciences, Faculty of Science and Technology, University Kebangsaan Malaysia, Bangi 43600, Selangor, MalaysiaLet 𝒜 be the class of analytic functions in the open unit disk . We define Θα,β:𝒜→𝒜 by (Θα,βf)(z):=Γ(2−α)zαDzα(Γ(2−β)zβDzβf(z)),(α,β≠2,3,4…), where Dzγf 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.http://dx.doi.org/10.1155/2009/597292 |
| spellingShingle | Oqlah Al-Refai Maslina Darus An Extension to the Owa-Srivastava Fractional Operator with Applications to Parabolic Starlike and Uniformly Convex Functions International Journal of Differential Equations |
| title | An Extension to the Owa-Srivastava Fractional Operator with Applications to Parabolic Starlike and Uniformly Convex Functions |
| title_full | An Extension to the Owa-Srivastava Fractional Operator with Applications to Parabolic Starlike and Uniformly Convex Functions |
| title_fullStr | An Extension to the Owa-Srivastava Fractional Operator with Applications to Parabolic Starlike and Uniformly Convex Functions |
| title_full_unstemmed | An Extension to the Owa-Srivastava Fractional Operator with Applications to Parabolic Starlike and Uniformly Convex Functions |
| title_short | An Extension to the Owa-Srivastava Fractional Operator with Applications to Parabolic Starlike and Uniformly Convex Functions |
| title_sort | extension to the owa srivastava fractional operator with applications to parabolic starlike and uniformly convex functions |
| url | http://dx.doi.org/10.1155/2009/597292 |
| work_keys_str_mv | AT oqlahalrefai anextensiontotheowasrivastavafractionaloperatorwithapplicationstoparabolicstarlikeanduniformlyconvexfunctions AT maslinadarus anextensiontotheowasrivastavafractionaloperatorwithapplicationstoparabolicstarlikeanduniformlyconvexfunctions AT oqlahalrefai extensiontotheowasrivastavafractionaloperatorwithapplicationstoparabolicstarlikeanduniformlyconvexfunctions AT maslinadarus extensiontotheowasrivastavafractionaloperatorwithapplicationstoparabolicstarlikeanduniformlyconvexfunctions |