On a combination of fractional differential and integral operators associated with a class of normalized functions

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

doi:10.3934/math.2021249

AIMS Mathematics

2021, Volume 6, Issue 4: 4211-4226. doi: 10.3934/math.2021249

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Research article

On a combination of fractional differential and integral operators associated with a class of normalized functions

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

1.
IEEE Membership: 94086547
2.
Department of Mathematics, Cankaya University, 06530 Balgat, Ankara, Turkey
3.
Institute of Space Sciences, R76900 Magurele-Bucharest, Romania
4.
Department of Medical Research, China Medical University, Taichung 40402, Taiwan

Received: 17 August 2020 Accepted: 01 February 2021 Published: 07 February 2021
MSC : 30C45, 30C55

Recently, the combined fractional operator (CFO) is introduced and discussed in Baleanu et al. ^[1] in real domain. In this paper, we extend CFO to the complex domain and study its geometric properties in some normalized analytic functions including the starlike and convex functions. Moreover, we employ the complex CFO to modify a class of Briot-Bouquet differential equations in a complex region. As a consequence, the upper solution is illustrated by using the concept of subordination inequality.
- fractional calculus,
- fractional differential operator,
- univalent function,
- analytic function,
- subordination and superordination,
- open unit disk,
- Briot-Bouquet differential equation
Citation: Rabha W. Ibrahim, Dumitru Baleanu. On a combination of fractional differential and integral operators associated with a class of normalized functions[J]. AIMS Mathematics, 2021, 6(4): 4211-4226. doi: 10.3934/math.2021249

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Abstract

Recently, the combined fractional operator (CFO) is introduced and discussed in Baleanu et al. ^[1] in real domain. In this paper, we extend CFO to the complex domain and study its geometric properties in some normalized analytic functions including the starlike and convex functions. Moreover, we employ the complex CFO to modify a class of Briot-Bouquet differential equations in a complex region. As a consequence, the upper solution is illustrated by using the concept of subordination inequality.

References

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