Generalized Fractional Integral Operator in a Complex Domain

Authors

  • Dalia S. ALI Medical Instrumentation Technology Engineering, Al-Mansour University College, Baghdad, Iraq. Email: dalia.sami@muc.edu.iq.
  • Rabha W. IBRAHIM Department of Mathematics, Near East University, Mathematics Research Center, Nicosia/Mersin, Turkey. Email: rabhaibrahim@yahoo.com. https://orcid.org/0000-0001-9341-025X
  • Dumitru BĂLEANU Department of Computer Science and Mathematics, Lebanese American University, Beirut, Lebanon; Institute of Space Sciences, Măgurele/Bucharest, Romania. Email: dumitru@cankaya.edu.tr. https://orcid.org/0000-0002-0286-7244
  • Nadia M.G. AL-SAIDI Department of Applied Sciences, University of Technology, Baghdad, Iraq. Email: ghanim@uotechnology.edu.iq. https://orcid.org/0000-0002-7255-5246

DOI:

https://doi.org/10.24193/subbmath.2024.2.03

Keywords:

Analytic function, subordination and superordination, univalent function, open unit disk, fractional integral operator, convolution operator, fractional calculus

Abstract

A new fractional integral operator is used to present a generalized class of analytic functions in a complex domain. The method of definition is based on a Hadamard product of analytic function, which is called convolution product. Then we formulate a convolution integral operator acting on the sub-class of normalized analytic functions. Consequently, we investigate the suggested convolution operator geometrically. Differential subordination inequalities, taking the starlike formula are given. Some consequences of well-known results are illustrated.

Mathematics Subject Classification (2010): 30C45.

Received 16 June 2022; Accepted 12 September 2022.

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Published

2024-06-18

How to Cite

ALI, D. S., IBRAHIM, R. W., BĂLEANU, D. ., & AL-SAIDI, N. M. (2024). Generalized Fractional Integral Operator in a Complex Domain. Studia Universitatis Babeș-Bolyai Mathematica, 69(2), 283–298. https://doi.org/10.24193/subbmath.2024.2.03

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