On a combination of fractional differential and integral operators associated with a class of normalized functions
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 emp...
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AIMS Press
2021-02-01
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| Series: | AIMS Mathematics |
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| Online Access: | http://www.aimspress.com/article/doi/10.3934/math.2021249?viewType=HTML |
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doaj-c30f5ecad6944a108b7f73d7dedf0d022021-02-24T02:02:05ZengAIMS PressAIMS Mathematics2473-69882021-02-01644211422610.3934/math.2021249On a combination of fractional differential and integral operators associated with a class of normalized functionsRabha W. Ibrahim0Dumitru Baleanu11. IEEE Membership: 940865472. 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, TaiwanRecently, 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.http://www.aimspress.com/article/doi/10.3934/math.2021249?viewType=HTMLfractional calculusfractional differential operatorunivalent functionanalytic functionsubordination and superordinationopen unit diskbriot-bouquet differential equation |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
Rabha W. Ibrahim Dumitru Baleanu |
| spellingShingle |
Rabha W. Ibrahim Dumitru Baleanu On a combination of fractional differential and integral operators associated with a class of normalized functions AIMS Mathematics fractional calculus fractional differential operator univalent function analytic function subordination and superordination open unit disk briot-bouquet differential equation |
| author_facet |
Rabha W. Ibrahim Dumitru Baleanu |
| author_sort |
Rabha W. Ibrahim |
| title |
On a combination of fractional differential and integral operators associated with a class of normalized functions |
| title_short |
On a combination of fractional differential and integral operators associated with a class of normalized functions |
| title_full |
On a combination of fractional differential and integral operators associated with a class of normalized functions |
| title_fullStr |
On a combination of fractional differential and integral operators associated with a class of normalized functions |
| title_full_unstemmed |
On a combination of fractional differential and integral operators associated with a class of normalized functions |
| title_sort |
on a combination of fractional differential and integral operators associated with a class of normalized functions |
| publisher |
AIMS Press |
| series |
AIMS Mathematics |
| issn |
2473-6988 |
| publishDate |
2021-02-01 |
| description |
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. |
| topic |
fractional calculus fractional differential operator univalent function analytic function subordination and superordination open unit disk briot-bouquet differential equation |
| url |
http://www.aimspress.com/article/doi/10.3934/math.2021249?viewType=HTML |
| work_keys_str_mv |
AT rabhawibrahim onacombinationoffractionaldifferentialandintegraloperatorsassociatedwithaclassofnormalizedfunctions AT dumitrubaleanu onacombinationoffractionaldifferentialandintegraloperatorsassociatedwithaclassofnormalizedfunctions |
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1724253509348491264 |