On Transformation Involving Basic Analogue to the Aleph-Function of Two Variables
In our work, we derived the fractional order <i>q</i>-integrals and <i>q</i>-derivatives concerning a basic analogue to the Aleph-function of two variables (AFTV). We discussed a related application and the <i>q</i>-extension of the corresponding Leibniz rule. Fin...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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MDPI AG
2022-01-01
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| Series: | Fractal and Fractional |
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| Online Access: | https://www.mdpi.com/2504-3110/6/2/71 |
| _version_ | 1797480108774129664 |
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| author | Dinesh Kumar Dumitru Baleanu Frédéric Ayant Norbert Südland |
| author_facet | Dinesh Kumar Dumitru Baleanu Frédéric Ayant Norbert Südland |
| author_sort | Dinesh Kumar |
| collection | DOAJ |
| description | In our work, we derived the fractional order <i>q</i>-integrals and <i>q</i>-derivatives concerning a basic analogue to the Aleph-function of two variables (AFTV). We discussed a related application and the <i>q</i>-extension of the corresponding Leibniz rule. Finally, we presented two corollaries concerning the basic analogue to the <i>I</i>-function of two variables and the basic analogue to the Aleph-function of one variable. |
| first_indexed | 2024-03-09T21:55:36Z |
| format | Article |
| id | doaj.art-46d8a8f740c545c793fc474c8b0f9071 |
| institution | Directory Open Access Journal |
| issn | 2504-3110 |
| language | English |
| last_indexed | 2024-03-09T21:55:36Z |
| publishDate | 2022-01-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Fractal and Fractional |
| spelling | doaj.art-46d8a8f740c545c793fc474c8b0f90712023-11-23T19:58:43ZengMDPI AGFractal and Fractional2504-31102022-01-01627110.3390/fractalfract6020071On Transformation Involving Basic Analogue to the Aleph-Function of Two VariablesDinesh Kumar0Dumitru Baleanu1Frédéric Ayant2Norbert Südland3Department of Applied Sciences, College of Agriculture-Jodhpur, Agriculture University Jodhpur, Jodhpur 342304, IndiaDepartment of Mathematics, Cankaya University, Ankara 06530, TurkeyCollége Jean L’Herminier, Allée des Nymphéas, 83500 La Seyne-sur-Mer, FranceAage GmbH, Röntgenstraße 24, 73431 Aalen, Baden-Württemberg, GermanyIn our work, we derived the fractional order <i>q</i>-integrals and <i>q</i>-derivatives concerning a basic analogue to the Aleph-function of two variables (AFTV). We discussed a related application and the <i>q</i>-extension of the corresponding Leibniz rule. Finally, we presented two corollaries concerning the basic analogue to the <i>I</i>-function of two variables and the basic analogue to the Aleph-function of one variable.https://www.mdpi.com/2504-3110/6/2/71Fractional <i>q</i>-integral<i>q</i>-derivative operatorsbasic analogue to the Aleph-functionbasic analogue to the <i>I</i>-function<i>q</i>-Leibniz rule |
| spellingShingle | Dinesh Kumar Dumitru Baleanu Frédéric Ayant Norbert Südland On Transformation Involving Basic Analogue to the Aleph-Function of Two Variables Fractal and Fractional Fractional <i>q</i>-integral <i>q</i>-derivative operators basic analogue to the Aleph-function basic analogue to the <i>I</i>-function <i>q</i>-Leibniz rule |
| title | On Transformation Involving Basic Analogue to the Aleph-Function of Two Variables |
| title_full | On Transformation Involving Basic Analogue to the Aleph-Function of Two Variables |
| title_fullStr | On Transformation Involving Basic Analogue to the Aleph-Function of Two Variables |
| title_full_unstemmed | On Transformation Involving Basic Analogue to the Aleph-Function of Two Variables |
| title_short | On Transformation Involving Basic Analogue to the Aleph-Function of Two Variables |
| title_sort | on transformation involving basic analogue to the aleph function of two variables |
| topic | Fractional <i>q</i>-integral <i>q</i>-derivative operators basic analogue to the Aleph-function basic analogue to the <i>I</i>-function <i>q</i>-Leibniz rule |
| url | https://www.mdpi.com/2504-3110/6/2/71 |
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