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

AIMS Mathematics

Rabha W. Ibrahim¹  Dumitru Baleanu² 

[1] 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;

关键词: fractional calculus;    fractional differential operator;    univalent function;    analytic function;    subordination and superordination;    open unit disk;    briot-bouquet differential equation;   

DOI  :  10.3934/math.2021249

来源: DOAJ

【 摘 要 】

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.

【 授权许可】

Unknown