Some Results on Third-Order Differential Subordination and Differential Superordination for Analytic Functions Using a Fractional Differential Operator

Faten Fakher Abdulnabi, Hiba F. Al-Janaby, Firas Ghanim and Alina Alb Lupaș ()
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Faten Fakher Abdulnabi: Department of Mathematics, College of Science, University of Baghdad, Baghdad 10071, Iraq
Hiba F. Al-Janaby: Department of Mathematics, College of Science, University of Baghdad, Baghdad 10071, Iraq
Firas Ghanim: Department of Mathematics, College of Sciences, University of Sharjah, Sharjah 27272, United Arab Emirates
Alina Alb Lupaș: Department of Mathematics and Computer Science, University of Oradea, 1 Universitatii Street, 410087 Oradea, Romania

Mathematics, 2023, vol. 11, issue 18, 1-14

Abstract: In this study, we explore the implications of a third-order differential subordination in the context of analytic functions associated with fractional differential operators. Our investigation involves the consideration of specific admissible classes of third-order differential functions. We also extend this exploration to establish a dual principle, resulting in a sandwich-type outcome. We introduce these admissible function classes by employing the fractional derivative operator D z α S N , S ϑ z and derive conditions on the normalized analytic function f that lead to sandwich-type subordination in combination with an appropriate fractional differential operator.

Keywords: analytic functions; differential subordination; differential superordination; best dominant; best subordinate; fractional derivative; 30C45 (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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