Some applications of fractional calculus for analytic functions

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UYANIK N., Owa S.

TURKISH JOURNAL OF MATHEMATICS, vol.45, no.5, pp.2025-2034, 2021 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 45 Issue: 5
  • Publication Date: 2021
  • Doi Number: 10.3906/mat-2103-23
  • Journal Name: TURKISH JOURNAL OF MATHEMATICS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, MathSciNet, zbMATH, TR DİZİN (ULAKBİM)
  • Page Numbers: pp.2025-2034
  • Keywords: Analytic function, fractional integral, fractional derivative, Miller and Mocanu lemma
  • Anadolu University Affiliated: Yes

Abstract

For analytic functions f (z) in the class A(n), fractional calculus (fractional integrals and fractional derivatives) D-z(lambda) f (z) of order lambda are introduced. Applying D-z(lambda) f (z) for f (z) is an element of A(n), we introduce the interesting subclass A(n) (alpha(m), beta, rho, lambda) of A(n). The object of this paper is to discuss some properties of f (z) concerning D-z(lambda) f (z).