Some Results on Third-Order Differential Subordination and Differential Superordination for Analytic Functions Using a Fractional Differential Operator
In this study, we explore the implications of a third-order differential subordination in the context of analytic functions associated with fractional differential operators. Our investigation involves the consideration of specific admissible classes of third-order differential functions. We also ex...
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| Format: | Article |
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MDPI AG
2023-09-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/11/18/4021 |
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| author | Faten Fakher Abdulnabi Hiba F. Al-Janaby Firas Ghanim Alina Alb Lupaș |
| author_facet | Faten Fakher Abdulnabi Hiba F. Al-Janaby Firas Ghanim Alina Alb Lupaș |
| author_sort | Faten Fakher Abdulnabi |
| collection | DOAJ |
| description | In this study, we explore the implications of a third-order differential subordination in the context of analytic functions associated with fractional differential operators. Our investigation involves the consideration of specific admissible classes of third-order differential functions. We also extend this exploration to establish a dual principle, resulting in a sandwich-type outcome. We introduce these admissible function classes by employing the fractional derivative operator <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mrow><msubsup><mrow><mi mathvariant="script">D</mi></mrow><mrow><mi>z</mi></mrow><mrow><mi>α</mi></mrow></msubsup><mi mathvariant="fraktur">S</mi></mrow><mrow><mi mathvariant="script">N</mi><mo>,</mo><mi mathvariant="script">S</mi></mrow></msub><mi>ϑ</mi><mfenced separators="|"><mrow><mi>z</mi></mrow></mfenced><mo> </mo></mrow></semantics></math></inline-formula> and derive conditions on the normalized analytic function <i>f</i> that lead to sandwich-type subordination in combination with an appropriate fractional differential operator. |
| first_indexed | 2024-03-10T22:29:13Z |
| format | Article |
| id | doaj.art-a37ac1df284a4e339cea02b9413b7b0c |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-10T22:29:13Z |
| publishDate | 2023-09-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-a37ac1df284a4e339cea02b9413b7b0c2023-11-19T11:50:49ZengMDPI AGMathematics2227-73902023-09-011118402110.3390/math11184021Some Results on Third-Order Differential Subordination and Differential Superordination for Analytic Functions Using a Fractional Differential OperatorFaten Fakher Abdulnabi0Hiba F. Al-Janaby1Firas Ghanim2Alina Alb Lupaș3Department of Mathematics, College of Science, University of Baghdad, Baghdad 10071, IraqDepartment of Mathematics, College of Science, University of Baghdad, Baghdad 10071, IraqDepartment of Mathematics, College of Sciences, University of Sharjah, Sharjah 27272, United Arab EmiratesDepartment of Mathematics and Computer Science, University of Oradea, 1 Universitatii Street, 410087 Oradea, RomaniaIn this study, we explore the implications of a third-order differential subordination in the context of analytic functions associated with fractional differential operators. Our investigation involves the consideration of specific admissible classes of third-order differential functions. We also extend this exploration to establish a dual principle, resulting in a sandwich-type outcome. We introduce these admissible function classes by employing the fractional derivative operator <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mrow><msubsup><mrow><mi mathvariant="script">D</mi></mrow><mrow><mi>z</mi></mrow><mrow><mi>α</mi></mrow></msubsup><mi mathvariant="fraktur">S</mi></mrow><mrow><mi mathvariant="script">N</mi><mo>,</mo><mi mathvariant="script">S</mi></mrow></msub><mi>ϑ</mi><mfenced separators="|"><mrow><mi>z</mi></mrow></mfenced><mo> </mo></mrow></semantics></math></inline-formula> and derive conditions on the normalized analytic function <i>f</i> that lead to sandwich-type subordination in combination with an appropriate fractional differential operator.https://www.mdpi.com/2227-7390/11/18/4021analytic functionsdifferential subordinationdifferential superordinationbest dominantbest subordinatefractional derivative |
| spellingShingle | Faten Fakher Abdulnabi Hiba F. Al-Janaby Firas Ghanim Alina Alb Lupaș Some Results on Third-Order Differential Subordination and Differential Superordination for Analytic Functions Using a Fractional Differential Operator Mathematics analytic functions differential subordination differential superordination best dominant best subordinate fractional derivative |
| title | Some Results on Third-Order Differential Subordination and Differential Superordination for Analytic Functions Using a Fractional Differential Operator |
| title_full | Some Results on Third-Order Differential Subordination and Differential Superordination for Analytic Functions Using a Fractional Differential Operator |
| title_fullStr | Some Results on Third-Order Differential Subordination and Differential Superordination for Analytic Functions Using a Fractional Differential Operator |
| title_full_unstemmed | Some Results on Third-Order Differential Subordination and Differential Superordination for Analytic Functions Using a Fractional Differential Operator |
| title_short | Some Results on Third-Order Differential Subordination and Differential Superordination for Analytic Functions Using a Fractional Differential Operator |
| title_sort | some results on third order differential subordination and differential superordination for analytic functions using a fractional differential operator |
| topic | analytic functions differential subordination differential superordination best dominant best subordinate fractional derivative |
| url | https://www.mdpi.com/2227-7390/11/18/4021 |
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