A Bicomplex Proportional Fractional (<i>ϑ</i>,<i>φ</i>)-Weighted Cauchy–Riemann Operator Using Riemann–Liouville Derivatives with Respect to an Hyperbolic-Valued Function
Based on the Riemann–Liouville derivatives with respect to functions taking values in the set of hyperbolic numbers, we consider a new bicomplex proportional fractional <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics>...
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MDPI AG
2024-12-01
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| Series: | Fractal and Fractional |
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| Online Access: | https://www.mdpi.com/2504-3110/9/1/1 |
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| author | José Oscar González-Cervantes Juan Bory-Reyes Juan Adrián Ramírez-Belman |
| author_facet | José Oscar González-Cervantes Juan Bory-Reyes Juan Adrián Ramírez-Belman |
| author_sort | José Oscar González-Cervantes |
| collection | DOAJ |
| description | Based on the Riemann–Liouville derivatives with respect to functions taking values in the set of hyperbolic numbers, we consider a new bicomplex proportional fractional <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>(</mo><mi>ϑ</mi><mo>,</mo><mi>φ</mi><mo>)</mo></mrow></semantics></math></inline-formula>-weighted Cauchy–Riemann operator, involving orthogonal bicomplex functions as weights, and its associated fractional Borel–Pompeiu formula is proved as the main result. |
| format | Article |
| id | doaj-art-203da4dea695439689eead0b7451a6b4 |
| 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-203da4dea695439689eead0b7451a6b42025-01-24T13:33:19ZengMDPI AGFractal and Fractional2504-31102024-12-0191110.3390/fractalfract9010001A Bicomplex Proportional Fractional (<i>ϑ</i>,<i>φ</i>)-Weighted Cauchy–Riemann Operator Using Riemann–Liouville Derivatives with Respect to an Hyperbolic-Valued FunctionJosé Oscar González-Cervantes0Juan Bory-Reyes1Juan Adrián Ramírez-Belman2Departamento de Matemáticas, ESFM-Instituto Politécnico Nacional, Ciudad México 07338, MexicoSEPI, ESIME-Zacatenco-Instituto Politécnico Nacional, Ciudad México 07338, MexicoSEPI, ESFM-Instituto Politécnico Nacional, Ciudad México 07338, MexicoBased on the Riemann–Liouville derivatives with respect to functions taking values in the set of hyperbolic numbers, we consider a new bicomplex proportional fractional <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>(</mo><mi>ϑ</mi><mo>,</mo><mi>φ</mi><mo>)</mo></mrow></semantics></math></inline-formula>-weighted Cauchy–Riemann operator, involving orthogonal bicomplex functions as weights, and its associated fractional Borel–Pompeiu formula is proved as the main result.https://www.mdpi.com/2504-3110/9/1/1bicomplex analysisproportional fractional integralsderivatives with respect to another functionRiemann–Liouville derivativesCauchy–Riemann operatorBorel–Pompeiu formula |
| spellingShingle | José Oscar González-Cervantes Juan Bory-Reyes Juan Adrián Ramírez-Belman A Bicomplex Proportional Fractional (<i>ϑ</i>,<i>φ</i>)-Weighted Cauchy–Riemann Operator Using Riemann–Liouville Derivatives with Respect to an Hyperbolic-Valued Function Fractal and Fractional bicomplex analysis proportional fractional integrals derivatives with respect to another function Riemann–Liouville derivatives Cauchy–Riemann operator Borel–Pompeiu formula |
| title | A Bicomplex Proportional Fractional (<i>ϑ</i>,<i>φ</i>)-Weighted Cauchy–Riemann Operator Using Riemann–Liouville Derivatives with Respect to an Hyperbolic-Valued Function |
| title_full | A Bicomplex Proportional Fractional (<i>ϑ</i>,<i>φ</i>)-Weighted Cauchy–Riemann Operator Using Riemann–Liouville Derivatives with Respect to an Hyperbolic-Valued Function |
| title_fullStr | A Bicomplex Proportional Fractional (<i>ϑ</i>,<i>φ</i>)-Weighted Cauchy–Riemann Operator Using Riemann–Liouville Derivatives with Respect to an Hyperbolic-Valued Function |
| title_full_unstemmed | A Bicomplex Proportional Fractional (<i>ϑ</i>,<i>φ</i>)-Weighted Cauchy–Riemann Operator Using Riemann–Liouville Derivatives with Respect to an Hyperbolic-Valued Function |
| title_short | A Bicomplex Proportional Fractional (<i>ϑ</i>,<i>φ</i>)-Weighted Cauchy–Riemann Operator Using Riemann–Liouville Derivatives with Respect to an Hyperbolic-Valued Function |
| title_sort | bicomplex proportional fractional i ϑ i i φ i weighted cauchy riemann operator using riemann liouville derivatives with respect to an hyperbolic valued function |
| topic | bicomplex analysis proportional fractional integrals derivatives with respect to another function Riemann–Liouville derivatives Cauchy–Riemann operator Borel–Pompeiu formula |
| url | https://www.mdpi.com/2504-3110/9/1/1 |
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