### Abstract

In this note, we discuss some properties of univalent solutions for fractional differential equation in the unit disk in the sense of Srivastava-Owa operators. By employing the differential subordination concept, we will study the upper bound of these solutions. Furthermore, by applying the Rogosinski theorem and Goluzin theorem, we illustrate some inequalities involving the coefficients and integral representation of these solutions. Moreover, the uniqueness is studied by using Rouche's theorem.

Original language | English |
---|---|

Pages (from-to) | 167-172 |

Number of pages | 6 |

Journal | Proceedings of the Pakistan Academy of Sciences |

Volume | 50 |

Issue number | 2 |

Publication status | Published - Jun 2013 |

### Keywords

- Analytic function
- Fractional calculus
- Fractional differential equation
- Subordination
- Superordination
- Unit disk
- Univalent function

### ASJC Scopus subject areas

- Social Sciences(all)

### Cite this

*Proceedings of the Pakistan Academy of Sciences*,

*50*(2), 167-172.

**Properties of univalent solution for complex fractional differential equation.** / Ibrahim, Rabha W.; Darus, Maslina.

Research output: Contribution to journal › Article

*Proceedings of the Pakistan Academy of Sciences*, vol. 50, no. 2, pp. 167-172.

}

TY - JOUR

T1 - Properties of univalent solution for complex fractional differential equation

AU - Ibrahim, Rabha W.

AU - Darus, Maslina

PY - 2013/6

Y1 - 2013/6

N2 - In this note, we discuss some properties of univalent solutions for fractional differential equation in the unit disk in the sense of Srivastava-Owa operators. By employing the differential subordination concept, we will study the upper bound of these solutions. Furthermore, by applying the Rogosinski theorem and Goluzin theorem, we illustrate some inequalities involving the coefficients and integral representation of these solutions. Moreover, the uniqueness is studied by using Rouche's theorem.

AB - In this note, we discuss some properties of univalent solutions for fractional differential equation in the unit disk in the sense of Srivastava-Owa operators. By employing the differential subordination concept, we will study the upper bound of these solutions. Furthermore, by applying the Rogosinski theorem and Goluzin theorem, we illustrate some inequalities involving the coefficients and integral representation of these solutions. Moreover, the uniqueness is studied by using Rouche's theorem.

KW - Analytic function

KW - Fractional calculus

KW - Fractional differential equation

KW - Subordination

KW - Superordination

KW - Unit disk

KW - Univalent function

UR - http://www.scopus.com/inward/record.url?scp=84879135060&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84879135060&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:84879135060

VL - 50

SP - 167

EP - 172

JO - Proceedings of the Pakistan Academy of Sciences

JF - Proceedings of the Pakistan Academy of Sciences

SN - 0377-2969

IS - 2

ER -