数学物理学报(英文版) ›› 2014, Vol. 34 ›› Issue (5): 1417-1426.doi: 10.1016/S0252-9602(14)60093-X

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ON A NEW CLASS OF ANALYTIC FUNCTION DERIVED BY A FRACTIONAL DIFFERENTIAL OPERATOR

Rabha W. IBRAHIM|Janusz SOK´O L   

  1. Institute of Mathematical Sciences, University Malaya, 50603, Malaysia; Department of Mathematics, Rzesz´ow University of Technology, ul. W. Pola 2, 35-959 Rzesz´ow, Poland
  • 收稿日期:2013-07-22 修回日期:2013-10-08 出版日期:2014-09-20 发布日期:2014-09-20

ON A NEW CLASS OF ANALYTIC FUNCTION DERIVED BY A FRACTIONAL DIFFERENTIAL OPERATOR

Rabha W. IBRAHIM|Janusz SOK´O L   

  1. Institute of Mathematical Sciences, University Malaya, 50603, Malaysia; Department of Mathematics, Rzesz´ow University of Technology, ul. W. Pola 2, 35-959 Rzesz´ow, Poland
  • Received:2013-07-22 Revised:2013-10-08 Online:2014-09-20 Published:2014-09-20

摘要:

Making use of the fractional differential operator, we impose and study a new class of analytic functions in the unit disk (type fractional differential equation). The main object of this paper is to investigate inclusion relations, coefficient bound for this class. Moreover, we discuss some geometric properties of the fractional differential operator.

关键词: analytic function, fractional calculus, fractional differential operator, univalent function, unit disk, bounded turning function

Abstract:

Making use of the fractional differential operator, we impose and study a new class of analytic functions in the unit disk (type fractional differential equation). The main object of this paper is to investigate inclusion relations, coefficient bound for this class. Moreover, we discuss some geometric properties of the fractional differential operator.

Key words: analytic function, fractional calculus, fractional differential operator, univalent function, unit disk, bounded turning function

中图分类号: 

  • 30C45