Fractional operators on the bounded symmetric domains of the Bergman spaces

Rabha W. Ibrahim; Dumitru Baleanu; Rabha W. Ibrahim; Dumitru Baleanu

doi:10.3934/math.2024188

AIMS Mathematics

2024, Volume 9, Issue 2: 3810-3835. doi: 10.3934/math.2024188

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Fractional operators on the bounded symmetric domains of the Bergman spaces

Rabha W. Ibrahim ^{1,2
,
,},
Dumitru Baleanu ^3,4

1.
Near East University, Mathematics Research Center, Department of Mathematics, Near East Boulevard, 99138, Nicosia, Turkey
2.
Information and Communication Technology Research Group, Scientific Research Center, Al-Ayen University, Thi-Qar, Iraq
3.
Department of Computer Science and Mathematics, Lebanese American University, Beirut, Lebanon
4.
Institute of Space Sciences, R76900 Magurele-Bucharest, Romania

Received: 16 August 2023 Revised: 21 September 2023 Accepted: 27 September 2023 Published: 11 January 2024
MSC : 30C55, 30C45

Mathematics has several uses for operators on bounded symmetric domains of Bergman spaces including complex geometry, functional analysis, harmonic analysis and operator theory. They offer instruments for examining the interaction between complex function theory and the underlying domain geometry. Here, we extend the Atangana-Baleanu fractional differential operator acting on a special type of class of analytic functions with the $ m $-fold symmetry characteristic in a bounded symmetric domain (we suggest the open unit disk). We explore the most significant geometric properties, including convexity and star-likeness. The boundedness in the weighted Bergman and the convex Bergman spaces associated with a bounded symmetric domain is investigated. A dual relations exist in these spaces. The subordination and superordination inequalities are presented. Our method is based on Young's convolution inequality.
- univalent function,
- subordination,
- superordination,
- open unit disk,
- fractional calculus,
- fractional differential operator,
- analytic function,
- fractional differential equation,
- symmetric domain
Citation: Rabha W. Ibrahim, Dumitru Baleanu. Fractional operators on the bounded symmetric domains of the Bergman spaces[J]. AIMS Mathematics, 2024, 9(2): 3810-3835. doi: 10.3934/math.2024188

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Abstract

Mathematics has several uses for operators on bounded symmetric domains of Bergman spaces including complex geometry, functional analysis, harmonic analysis and operator theory. They offer instruments for examining the interaction between complex function theory and the underlying domain geometry. Here, we extend the Atangana-Baleanu fractional differential operator acting on a special type of class of analytic functions with the $ m $-fold symmetry characteristic in a bounded symmetric domain (we suggest the open unit disk). We explore the most significant geometric properties, including convexity and star-likeness. The boundedness in the weighted Bergman and the convex Bergman spaces associated with a bounded symmetric domain is investigated. A dual relations exist in these spaces. The subordination and superordination inequalities are presented. Our method is based on Young's convolution inequality.

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