Analysis of Generalized Bessel–Maitland Function and Its Properties
In this article, we introduce the generalized Bessel–Maitland function (EGBMF) using the extended beta function and some important properties obtained. Thus, we first show interesting relationships of this function with Laguerre polynomials and the Whittaker functions. We also introduce and prove so...
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| Format: | Article |
| Language: | English |
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MDPI AG
2023-04-01
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| Series: | Axioms |
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| Online Access: | https://www.mdpi.com/2075-1680/12/4/356 |
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| author | Talha Usman Nabiullah Khan Francisco Martínez |
| author_facet | Talha Usman Nabiullah Khan Francisco Martínez |
| author_sort | Talha Usman |
| collection | DOAJ |
| description | In this article, we introduce the generalized Bessel–Maitland function (EGBMF) using the extended beta function and some important properties obtained. Thus, we first show interesting relationships of this function with Laguerre polynomials and the Whittaker functions. We also introduce and prove some properties of the derivatives associated with EGBMF. In this sense, we establish a result relative to the extended fractional derivatives of Riemann–Liouville. Furthermore, the Mellin transform of this function is evaluated in terms of the generalized Wright hypergeometric function, and its Euler transform is also obtained. Finally, we derive several graphical representations using the Gauss quadrature and the Laguerre–Gauss quadrature methods, which show that the numerical and theoretical simulations are consistent. The results derived from this research can be potentially useful in applications in several fields, in particular, physics, applied mathematics, and engineering. |
| first_indexed | 2024-03-11T05:14:55Z |
| format | Article |
| id | doaj.art-5a370c7bdcb748878d3f1533c06097c3 |
| institution | Directory Open Access Journal |
| issn | 2075-1680 |
| language | English |
| last_indexed | 2024-03-11T05:14:55Z |
| publishDate | 2023-04-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Axioms |
| spelling | doaj.art-5a370c7bdcb748878d3f1533c06097c32023-11-17T18:19:14ZengMDPI AGAxioms2075-16802023-04-0112435610.3390/axioms12040356Analysis of Generalized Bessel–Maitland Function and Its PropertiesTalha Usman0Nabiullah Khan1Francisco Martínez2Department of General Requirements, University of Technology and Applied Sciences, Sur 411, OmanDepartment of Applied Mathematics, Faculty of Engineering and Technology, Aligarh Muslim University, Aligarh 202002, IndiaDepartamento de Matemática Aplicada y Estadística, Universidad Politécnica de Cartagena, 30203 Cartagena, SpainIn this article, we introduce the generalized Bessel–Maitland function (EGBMF) using the extended beta function and some important properties obtained. Thus, we first show interesting relationships of this function with Laguerre polynomials and the Whittaker functions. We also introduce and prove some properties of the derivatives associated with EGBMF. In this sense, we establish a result relative to the extended fractional derivatives of Riemann–Liouville. Furthermore, the Mellin transform of this function is evaluated in terms of the generalized Wright hypergeometric function, and its Euler transform is also obtained. Finally, we derive several graphical representations using the Gauss quadrature and the Laguerre–Gauss quadrature methods, which show that the numerical and theoretical simulations are consistent. The results derived from this research can be potentially useful in applications in several fields, in particular, physics, applied mathematics, and engineering.https://www.mdpi.com/2075-1680/12/4/356generalized Bessel–Maitland functionextended beta functionfractional derivativeMellin transformLaguerre polynomialsWhittaker functions |
| spellingShingle | Talha Usman Nabiullah Khan Francisco Martínez Analysis of Generalized Bessel–Maitland Function and Its Properties Axioms generalized Bessel–Maitland function extended beta function fractional derivative Mellin transform Laguerre polynomials Whittaker functions |
| title | Analysis of Generalized Bessel–Maitland Function and Its Properties |
| title_full | Analysis of Generalized Bessel–Maitland Function and Its Properties |
| title_fullStr | Analysis of Generalized Bessel–Maitland Function and Its Properties |
| title_full_unstemmed | Analysis of Generalized Bessel–Maitland Function and Its Properties |
| title_short | Analysis of Generalized Bessel–Maitland Function and Its Properties |
| title_sort | analysis of generalized bessel maitland function and its properties |
| topic | generalized Bessel–Maitland function extended beta function fractional derivative Mellin transform Laguerre polynomials Whittaker functions |
| url | https://www.mdpi.com/2075-1680/12/4/356 |
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