APPLICATIONS OF NON-HOMOGENEOUS CAUCHY-EULER FRACTIONAL q-DIFFERENTIAL EQUATION TO A NEW CLASS OF ANALYTIC FUNCTIONS

BULUT S.

Khayyam Journal of Mathematics, vol.9, no.2, pp.288-299, 2023 (Scopus) identifier

  • Publication Type: Article / Article
  • Volume: 9 Issue: 2
  • Publication Date: 2023
  • Doi Number: 10.22034/kjm.2023.390830.2818
  • Journal Name: Khayyam Journal of Mathematics
  • Journal Indexes: Scopus
  • Page Numbers: pp.288-299
  • Keywords: Analytic function, Cauchy-Euler differential equation, fractional q-derivative, q-convex function, q-starlike function
  • Kocaeli University Affiliated: Yes

Abstract

We define a new general fractional q-differential operator, and by means of this operator, we introduce a new subclass of analytic functions that are the solutions of the non-homogeneous Cauchy–Euler fractional q-differential equations. Our aim is to determine upper bounds of Taylor–Maclaurin coefficients for functions belong to this class.