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Research Article | Open Access

Subclasses of spiral-like functions associated with the modified Caputo's derivative operator

Jamal Salah1( ), Hameed Ur Rehman2, Iman Al Buwaiqi1, Ahmad Al Azab1, Maryam Al Hashmi1
Department of Basic Science, College of Health and Applied Sciences, A'Sharqiyah University, Ibra Oman
Center for Language and Foundation Studies, A'Sharqiyah University, Ibra Oman
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Abstract

In this paper, the authors apply the modified Caputo's derivative operator, to introduce two new subclasses of spiral-like functions, namely the spiral-starlike functions and spiral-convex functions. In addition to this we, elaborate on the inclusion properties of these subclasses by considering the generalization of the Mittag-Leffler function and its integral transformation. Consequently, we obtain the subordination result for the functions in the class of spiral-like functions.

Keywords

spiral-like functionsubordinationMittag-Leffler functionfractional calculusCaputo's derivative operator
CLC number: 30C45, 30C50

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AIMS Mathematics
Volume 8 Issue 8,
August 2023
Pages 18474-18490
DOI: 10.3934/math.2023939

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Cite this article:
Salah J, Rehman HU, Al Buwaiqi I, et al. Subclasses of spiral-like functions associated with the modified Caputo's derivative operator. AIMS Mathematics, 2023, 8(8): 18474-18490. https://doi.org/10.3934/math.2023939

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Received: 06 March 2023
Revised: 11 May 2023
Accepted: 17 May 2023
Published: 15 August 2023
©2023 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0)