Differential operator generalized by fractional derivatives

Rabha W. Ibrahim, Maslina Darus

Research output: Contribution to journalArticle

6 Citations (Scopus)

Abstract

By using the fractional derivative operator of Owa and Srivastava, we define a new linear multiplier fractional differential operator. Some generalized classes of analytic functions containing this multiplier are introduced. Basic properties of these classes are studied, such as inclusion relations and coefficient bounds. Some well known subclasses are pointed out as new special cases of our results. Moreover, the Cesáro partial sums σ m of functions f are considered, and sharp lower bounds for the ratios of real part of f and σ m (and also of f' and σ' m) are determined in the unit open disk.

Original languageEnglish
Pages (from-to)167-184
Number of pages18
JournalMiskolc Mathematical Notes
Volume12
Issue number2
Publication statusPublished - 2011

Fingerprint

Fractional Derivative
Multiplier
Differential operator
Coefficient Bounds
Derivatives
Inclusion Relations
Partial Sums
Mathematical operators
Analytic function
Fractional
Lower bound
Unit
Operator
Class

Keywords

  • Cesáro partial sums
  • Close to convex function
  • Convex function
  • Fractional derivative
  • Inclusion relations
  • Starlike function
  • Subordination
  • Superordination

ASJC Scopus subject areas

  • Algebra and Number Theory
  • Analysis
  • Control and Optimization
  • Discrete Mathematics and Combinatorics
  • Numerical Analysis

Cite this

Differential operator generalized by fractional derivatives. / Ibrahim, Rabha W.; Darus, Maslina.

In: Miskolc Mathematical Notes, Vol. 12, No. 2, 2011, p. 167-184.

Research output: Contribution to journalArticle

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