Geometric Properties and Hardy Spaces of Rabotnov Fractional Exponential Functions

The aim of this study is to investigate a certain sufficiency criterion for uniform convexity, strong starlikeness, and strong convexity of Rabtonov fractional exponential functions. We also study the starlikeness and convexity of order γ. Moreover, we find conditions so that the Rabotnov functions...

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Bibliographic Details
Published in:Fractal and fractional 2024-01, Vol.8 (1), p.5
Main Authors: Raza, Mohsan, Breaz, Daniel, Mushtaq, Saima, Cotîrlă, Luminiţa-Ioana, Tawfiq, Ferdous M. O., Rapeanu, Eleonora
Format: Article
Language:English
Subjects:
Analytic functions
Convex analysis
convex functions
Convexity
Exponential functions
Mathematical functions
Mechanics
Numerical analysis
Physics
Rabotnov function
starlike functions
strong convexity
strong starlikeness
uniformly convex functions
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Summary:The aim of this study is to investigate a certain sufficiency criterion for uniform convexity, strong starlikeness, and strong convexity of Rabtonov fractional exponential functions. We also study the starlikeness and convexity of order γ. Moreover, we find conditions so that the Rabotnov functions belong to the class of bounded analytic functions and Hardy spaces. Various consequences of these results are also presented.
ISSN:2504-3110
2504-3110
DOI:10.3390/fractalfract8010005