Conformable differential operator generalizes the Briot-Bouquet differential equation in a complex domain

Rabha W. Ibrahim; Jay M. Jahangiri; Rabha W. Ibrahim; Jay M. Jahangiri

doi:10.3934/math.2019.6.1582

AIMS Mathematics

2019, Volume 4, Issue 6: 1582-1595. doi: 10.3934/math.2019.6.1582

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Conformable differential operator generalizes the Briot-Bouquet differential equation in a complex domain

Rabha W. Ibrahim ^{1
,
,},
Jay M. Jahangiri ²

1.
Cloud Computing Center, University Malaya, 50603, Malaysia
2.
Mathematical Sciences, Kent State University, Burton, Ohio 44021-9500, USA

Received: 07 July 2019 Accepted: 25 September 2019 Published: 12 October 2019
MSC : 30C45, 30C55

Very recently, a new local and limit-based extension of derivatives, called conformable derivative, has been formulated. We define a new conformable derivative in the complex domain, derive its differential calculus properties as well as its geometric properties in the field of geometric function theory. In addition, we employ the new conformable operator to generalize the Briot-Bouquet differential equation. We establish analytic solutions for the generalized Briot-Bouquet differential equation by using the concept of subordination and superordination. Examples of special normalized functions are illustrated in the sequel.
- conformable derivative,
- subordination and superordination,
- univalent function,
- analytic function,
- Briot-Bouquet differential equation
Citation: Rabha W. Ibrahim, Jay M. Jahangiri. Conformable differential operator generalizes the Briot-Bouquet differential equation in a complex domain[J]. AIMS Mathematics, 2019, 4(6): 1582-1595. doi: 10.3934/math.2019.6.1582

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Abstract

Very recently, a new local and limit-based extension of derivatives, called conformable derivative, has been formulated. We define a new conformable derivative in the complex domain, derive its differential calculus properties as well as its geometric properties in the field of geometric function theory. In addition, we employ the new conformable operator to generalize the Briot-Bouquet differential equation. We establish analytic solutions for the generalized Briot-Bouquet differential equation by using the concept of subordination and superordination. Examples of special normalized functions are illustrated in the sequel.

References

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