New Applications of Fractional <i>q</i>-Calculus Operator for a New Subclass of <i>q</i>-Starlike Functions Related with the Cardioid Domain
Recently, a number of researchers from different fields have taken a keen interest in the domain of fractional <i>q</i>-calculus on the basis of fractional integrals and derivative operators. This has been used in various scientific research and technology fields, including optics, mathe...
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| Format: | Article |
| Language: | English |
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MDPI AG
2024-01-01
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| Series: | Fractal and Fractional |
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| Online Access: | https://www.mdpi.com/2504-3110/8/1/71 |
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| author | Mohammad Faisal Khan Mohammed AbaOud |
| author_facet | Mohammad Faisal Khan Mohammed AbaOud |
| author_sort | Mohammad Faisal Khan |
| collection | DOAJ |
| description | Recently, a number of researchers from different fields have taken a keen interest in the domain of fractional <i>q</i>-calculus on the basis of fractional integrals and derivative operators. This has been used in various scientific research and technology fields, including optics, mathematical biology, plasma physics, electromagnetic theory, and many more. This article explores some mathematical applications of the fractional <i>q</i>-differential and integral operator in the field of geometric function theory. By using the linear multiplier fractional <i>q</i>-differintegral operator <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msubsup><mi>D</mi><mrow><mi>q</mi><mo>,</mo><mi>λ</mi></mrow><mi>m</mi></msubsup><mfenced separators="" open="(" close=")"><mi>ρ</mi><mo>,</mo><mi>σ</mi></mfenced></mrow></semantics></math></inline-formula> and subordination, we define and develop a collection of <i>q</i>-starlike functions that are linked to the cardioid domain. This study also investigates sharp inequality problems like initial coefficient bounds, the Fekete–Szego problems, and the coefficient inequalities for a new class of <i>q</i>-starlike functions in the open unit disc <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi mathvariant="script">U</mi></semantics></math></inline-formula>. Furthermore, we analyze novel findings with respect to the inverse function <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>(</mo><msup><mi>μ</mi><mrow><mo>−</mo><mn>1</mn></mrow></msup><mo>)</mo></mrow></semantics></math></inline-formula> within the class of <i>q</i>-starlike functions in <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi mathvariant="script">U</mi></semantics></math></inline-formula>. The findings in this paper are easy to understand and show a connection between present and past studies. |
| first_indexed | 2024-03-08T10:54:59Z |
| format | Article |
| id | doaj.art-19a53002dbd54849a66409495485b43c |
| institution | Directory Open Access Journal |
| issn | 2504-3110 |
| language | English |
| last_indexed | 2024-03-08T10:54:59Z |
| publishDate | 2024-01-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Fractal and Fractional |
| spelling | doaj.art-19a53002dbd54849a66409495485b43c2024-01-26T16:36:44ZengMDPI AGFractal and Fractional2504-31102024-01-01817110.3390/fractalfract8010071New Applications of Fractional <i>q</i>-Calculus Operator for a New Subclass of <i>q</i>-Starlike Functions Related with the Cardioid DomainMohammad Faisal Khan0Mohammed AbaOud1Department of Basic Sciences, College of Science and Theoretical Studies, Saudi Electronic University, Riyadh 11673, Saudi ArabiaDepartment of Mathematics and Statistics, Imam Mohammad Ibn Saud Islamic University (IMSIU), Riyadh 11564, Saudi ArabiaRecently, a number of researchers from different fields have taken a keen interest in the domain of fractional <i>q</i>-calculus on the basis of fractional integrals and derivative operators. This has been used in various scientific research and technology fields, including optics, mathematical biology, plasma physics, electromagnetic theory, and many more. This article explores some mathematical applications of the fractional <i>q</i>-differential and integral operator in the field of geometric function theory. By using the linear multiplier fractional <i>q</i>-differintegral operator <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msubsup><mi>D</mi><mrow><mi>q</mi><mo>,</mo><mi>λ</mi></mrow><mi>m</mi></msubsup><mfenced separators="" open="(" close=")"><mi>ρ</mi><mo>,</mo><mi>σ</mi></mfenced></mrow></semantics></math></inline-formula> and subordination, we define and develop a collection of <i>q</i>-starlike functions that are linked to the cardioid domain. This study also investigates sharp inequality problems like initial coefficient bounds, the Fekete–Szego problems, and the coefficient inequalities for a new class of <i>q</i>-starlike functions in the open unit disc <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi mathvariant="script">U</mi></semantics></math></inline-formula>. Furthermore, we analyze novel findings with respect to the inverse function <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>(</mo><msup><mi>μ</mi><mrow><mo>−</mo><mn>1</mn></mrow></msup><mo>)</mo></mrow></semantics></math></inline-formula> within the class of <i>q</i>-starlike functions in <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi mathvariant="script">U</mi></semantics></math></inline-formula>. The findings in this paper are easy to understand and show a connection between present and past studies.https://www.mdpi.com/2504-3110/8/1/71analytic functions<i>q</i>-calculus<i>q</i>-starlike functionsfractional <i>q</i>-calculuscardioid domainsubordination |
| spellingShingle | Mohammad Faisal Khan Mohammed AbaOud New Applications of Fractional <i>q</i>-Calculus Operator for a New Subclass of <i>q</i>-Starlike Functions Related with the Cardioid Domain Fractal and Fractional analytic functions <i>q</i>-calculus <i>q</i>-starlike functions fractional <i>q</i>-calculus cardioid domain subordination |
| title | New Applications of Fractional <i>q</i>-Calculus Operator for a New Subclass of <i>q</i>-Starlike Functions Related with the Cardioid Domain |
| title_full | New Applications of Fractional <i>q</i>-Calculus Operator for a New Subclass of <i>q</i>-Starlike Functions Related with the Cardioid Domain |
| title_fullStr | New Applications of Fractional <i>q</i>-Calculus Operator for a New Subclass of <i>q</i>-Starlike Functions Related with the Cardioid Domain |
| title_full_unstemmed | New Applications of Fractional <i>q</i>-Calculus Operator for a New Subclass of <i>q</i>-Starlike Functions Related with the Cardioid Domain |
| title_short | New Applications of Fractional <i>q</i>-Calculus Operator for a New Subclass of <i>q</i>-Starlike Functions Related with the Cardioid Domain |
| title_sort | new applications of fractional i q i calculus operator for a new subclass of i q i starlike functions related with the cardioid domain |
| topic | analytic functions <i>q</i>-calculus <i>q</i>-starlike functions fractional <i>q</i>-calculus cardioid domain subordination |
| url | https://www.mdpi.com/2504-3110/8/1/71 |
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