On certain inclusion relations of functions with bounded rotations associated with Mittag-Leffler functions

Bushra Kanwal; Saqib Hussain; Thabet Abdeljawad; Bushra Kanwal; Saqib Hussain; Thabet Abdeljawad

doi:10.3934/math.2022440

AIMS Mathematics

2022, Volume 7, Issue 5: 7866-7887. doi: 10.3934/math.2022440

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Research article

On certain inclusion relations of functions with bounded rotations associated with Mittag-Leffler functions

1.
Department of Mathematics, COMSATS University Islamabad, Islamabad, Pakistan
2.
Department of Mathematical Sciences, Fatima Jinnah Women University, Rawalpindi, Pakistan
3.
Department of Mathematics, COMSATS University Islamabad, Abbottabad Campus 22060, Pakistan
4.
Department of Mathematics and Sciences, Prince Sultan University, P.O.Box 66833, Riyadh, Saudi Arabia
5.
Department of Medical Research, China Medical University, Taichung 40402, Taiwan

Received: 26 November 2021 Revised: 08 February 2022 Accepted: 13 February 2022 Published: 17 February 2022
MSC : 46S40, 47H10, 54H25

Inspired essentially by the excellence of the implementations of the Mittag-Leffler functions in numerous areas of science and engineering, the authors present, in a unified manner, a detailed account of the Mittag-Leffler function and generalized Mittag-Leffler functions and their interesting and useful characteristics. Besides that, we have used generalized Mittag-Leffler functions to define some novel classes associated with bounded boundary and bounded radius rotations. Moreover, several inclusion relations and radius results, along with some integral preserving properties of these newly constructed classes have been investigated. Our derived results are analogous to some of those already present in the literature. The results showed that the proposed findings procedure is dependable and meticulous in presenting the tendencies of subordination, super-ordination and fractional operators techniques.
- bounded boundary rotations,
- strongly Janowski type functions,
- subordination,
- generalized Mittag-Leffler functions
Citation: Bushra Kanwal, Saqib Hussain, Thabet Abdeljawad. On certain inclusion relations of functions with bounded rotations associated with Mittag-Leffler functions[J]. AIMS Mathematics, 2022, 7(5): 7866-7887. doi: 10.3934/math.2022440

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Abstract

Inspired essentially by the excellence of the implementations of the Mittag-Leffler functions in numerous areas of science and engineering, the authors present, in a unified manner, a detailed account of the Mittag-Leffler function and generalized Mittag-Leffler functions and their interesting and useful characteristics. Besides that, we have used generalized Mittag-Leffler functions to define some novel classes associated with bounded boundary and bounded radius rotations. Moreover, several inclusion relations and radius results, along with some integral preserving properties of these newly constructed classes have been investigated. Our derived results are analogous to some of those already present in the literature. The results showed that the proposed findings procedure is dependable and meticulous in presenting the tendencies of subordination, super-ordination and fractional operators techniques.

References

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