Sandwich-Type Results and Existence Results of Analytic Functions Associated with the Fractional <i>q</i>-Calculus Operator
In the present investigation, we present certain subordination and superordination results for the <i>q</i>-integral operator of a fractional order associated with analytic functions in the open unit disk <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML"...
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2024-12-01
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| Series: | Fractal and Fractional |
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| Online Access: | https://www.mdpi.com/2504-3110/9/1/4 |
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| author | Sudhansu Palei Madan Mohan Soren Daniel Breaz Luminiţa-Ioana Cotîrlǎ |
| author_facet | Sudhansu Palei Madan Mohan Soren Daniel Breaz Luminiţa-Ioana Cotîrlǎ |
| author_sort | Sudhansu Palei |
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| description | In the present investigation, we present certain subordination and superordination results for the <i>q</i>-integral operator of a fractional order associated with analytic functions in the open unit disk <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi mathvariant="bold">U</mi></semantics></math></inline-formula>. Using this <i>q</i>-integral operator, we obtain sandwich-type results. Furthermore, we employ the existence of univalent solutions to a <i>q</i>-differential equation connected with a fractional <i>q</i>-integral operator of fractional order. We use these results to demonstrate the significance of our findings for particular functions. We also derive some examples and corollaries that are pertinent to our results. |
| format | Article |
| id | doaj-art-e46a2c6ceddd449486e893e08d2faf6c |
| institution | Kabale University |
| issn | 2504-3110 |
| language | English |
| publishDate | 2024-12-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Fractal and Fractional |
| spelling | doaj-art-e46a2c6ceddd449486e893e08d2faf6c2025-01-24T13:33:20ZengMDPI AGFractal and Fractional2504-31102024-12-0191410.3390/fractalfract9010004Sandwich-Type Results and Existence Results of Analytic Functions Associated with the Fractional <i>q</i>-Calculus OperatorSudhansu Palei0Madan Mohan Soren1Daniel Breaz2Luminiţa-Ioana Cotîrlǎ3Department of Mathematics, Berhampur University, Berhampur 760007, Odisha, IndiaDepartment of Mathematics, Berhampur University, Berhampur 760007, Odisha, IndiaDepartment of Mathematics, “1 Decembrie 1918” University of Alba Iulia, 510009 Alba Iulia, RomaniaDepartment of Mathematics, Technical University of Cluj-Napoca, 400114 Cluj-Napoca, RomaniaIn the present investigation, we present certain subordination and superordination results for the <i>q</i>-integral operator of a fractional order associated with analytic functions in the open unit disk <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi mathvariant="bold">U</mi></semantics></math></inline-formula>. Using this <i>q</i>-integral operator, we obtain sandwich-type results. Furthermore, we employ the existence of univalent solutions to a <i>q</i>-differential equation connected with a fractional <i>q</i>-integral operator of fractional order. We use these results to demonstrate the significance of our findings for particular functions. We also derive some examples and corollaries that are pertinent to our results.https://www.mdpi.com/2504-3110/9/1/4analytic functionsfractional q-calculus operatorsdifferential subordinationdifferential superordinationsandwich-type resultsunivalent solution |
| spellingShingle | Sudhansu Palei Madan Mohan Soren Daniel Breaz Luminiţa-Ioana Cotîrlǎ Sandwich-Type Results and Existence Results of Analytic Functions Associated with the Fractional <i>q</i>-Calculus Operator Fractal and Fractional analytic functions fractional q-calculus operators differential subordination differential superordination sandwich-type results univalent solution |
| title | Sandwich-Type Results and Existence Results of Analytic Functions Associated with the Fractional <i>q</i>-Calculus Operator |
| title_full | Sandwich-Type Results and Existence Results of Analytic Functions Associated with the Fractional <i>q</i>-Calculus Operator |
| title_fullStr | Sandwich-Type Results and Existence Results of Analytic Functions Associated with the Fractional <i>q</i>-Calculus Operator |
| title_full_unstemmed | Sandwich-Type Results and Existence Results of Analytic Functions Associated with the Fractional <i>q</i>-Calculus Operator |
| title_short | Sandwich-Type Results and Existence Results of Analytic Functions Associated with the Fractional <i>q</i>-Calculus Operator |
| title_sort | sandwich type results and existence results of analytic functions associated with the fractional i q i calculus operator |
| topic | analytic functions fractional q-calculus operators differential subordination differential superordination sandwich-type results univalent solution |
| url | https://www.mdpi.com/2504-3110/9/1/4 |
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