The g-generalized Mittag-Leffler (p,s,k)-function
The Mittag-Leffler (ML) function exists in the study of special functions. It may be used to solve a variety of fractional differential equations (FDEs) including fractional Laplace and fractional Poisson equations. This paper introduces the generalization of ML function, hereafter referred to as th...
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| Format: | Article |
| Language: | English |
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Elsevier
2025-02-01
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| Series: | Alexandria Engineering Journal |
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| Online Access: | http://www.sciencedirect.com/science/article/pii/S1110016824015047 |
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| author | Umbreen Ayub Madiha Shafiq Amir Abbas Umair Khan Anuar Ishak Y.S. Hamed Homan Emadifar |
| author_facet | Umbreen Ayub Madiha Shafiq Amir Abbas Umair Khan Anuar Ishak Y.S. Hamed Homan Emadifar |
| author_sort | Umbreen Ayub |
| collection | DOAJ |
| description | The Mittag-Leffler (ML) function exists in the study of special functions. It may be used to solve a variety of fractional differential equations (FDEs) including fractional Laplace and fractional Poisson equations. This paper introduces the generalization of ML function, hereafter referred to as the g-generalized ML (p,s,k)-function, which extends the applicability of fractional calculus and complex analysis to a broader range of problems. The basic properties of the g-generalized ML (p,s,k)-function including its convergence, differentiability, and connection with the Wright hypergeometric and Fox H-functions, which is essential in various mathematical and scientific contexts are presented. The paper then delves into the utilization of the g-generalized ML (p,s,k)-function in integral transforms, with a focus on the Laplace and Fourier transforms. How the g-generalized ML (p,s,k)-function serves as a valuable tool to solve FDEs, including those that arise in engineering, physics, and biology are highlighted. |
| format | Article |
| id | doaj-art-27257fee079b4fad85d0670e23abd650 |
| institution | Kabale University |
| issn | 1110-0168 |
| language | English |
| publishDate | 2025-02-01 |
| publisher | Elsevier |
| record_format | Article |
| series | Alexandria Engineering Journal |
| spelling | doaj-art-27257fee079b4fad85d0670e23abd6502025-02-07T04:47:09ZengElsevierAlexandria Engineering Journal1110-01682025-02-01113565572The g-generalized Mittag-Leffler (p,s,k)-functionUmbreen Ayub0Madiha Shafiq1Amir Abbas2Umair Khan3Anuar Ishak4Y.S. Hamed5Homan Emadifar6Department of Mathematics, University of Sargodha, Sargodha 40100, PakistanDepartment of Mathematics, University of Sargodha, Sargodha 40100, Pakistan; Corresponding author.Department of Mathematics, Faculty of Natural Science and Technology, Baba Guru Nanak University, Nankana Sahib 39100, Pakistan; Department of Mathematics, Faculty of Science, University of Gujrat, Sub-Campus Mandi Bahauddin, Mandi Bahauddin 50400, PakistanDepartment of Mathematical Sciences, Faculty of Science and Technology, Universiti Kebangsaan Malaysia, UKM, Bangi 43600, Selangor, Malaysia; Department of Mathematics, Faculty of Science, Sakarya University, Serdivan/Sakarya 54050, Turkiye; Department of Computer Science and Mathematics, Lebanese American University, Byblos 1401, Lebanon; Department of Mechanics and Mathematics, Western Caspian University, Baku 1001, AzerbaijanDepartment of Mathematical Sciences, Faculty of Science and Technology, Universiti Kebangsaan Malaysia, UKM, Bangi 43600, Selangor, MalaysiaDepartment of Mathematics and Statistics, College of Science, Taif University, P.O. Box 11099, Taif 21944, Saudi ArabiaDepartment of Mathematics, Saveetha School of Engineering, Saveetha Institute of Medical and Technical Sciences, Saveetha University, Chennai 602 105, Tamil Nadu, India; MEU Research Unit, Middle East University, Amman 11831, JordanThe Mittag-Leffler (ML) function exists in the study of special functions. It may be used to solve a variety of fractional differential equations (FDEs) including fractional Laplace and fractional Poisson equations. This paper introduces the generalization of ML function, hereafter referred to as the g-generalized ML (p,s,k)-function, which extends the applicability of fractional calculus and complex analysis to a broader range of problems. The basic properties of the g-generalized ML (p,s,k)-function including its convergence, differentiability, and connection with the Wright hypergeometric and Fox H-functions, which is essential in various mathematical and scientific contexts are presented. The paper then delves into the utilization of the g-generalized ML (p,s,k)-function in integral transforms, with a focus on the Laplace and Fourier transforms. How the g-generalized ML (p,s,k)-function serves as a valuable tool to solve FDEs, including those that arise in engineering, physics, and biology are highlighted.http://www.sciencedirect.com/science/article/pii/S1110016824015047ML (p, s, k)-functiong-generalized ML (p, s, k)-functionWright hypergeometric functionFox H-functionIntegral transforms |
| spellingShingle | Umbreen Ayub Madiha Shafiq Amir Abbas Umair Khan Anuar Ishak Y.S. Hamed Homan Emadifar The g-generalized Mittag-Leffler (p,s,k)-function Alexandria Engineering Journal ML (p, s, k)-function g-generalized ML (p, s, k)-function Wright hypergeometric function Fox H-function Integral transforms |
| title | The g-generalized Mittag-Leffler (p,s,k)-function |
| title_full | The g-generalized Mittag-Leffler (p,s,k)-function |
| title_fullStr | The g-generalized Mittag-Leffler (p,s,k)-function |
| title_full_unstemmed | The g-generalized Mittag-Leffler (p,s,k)-function |
| title_short | The g-generalized Mittag-Leffler (p,s,k)-function |
| title_sort | g generalized mittag leffler p s k function |
| topic | ML (p, s, k)-function g-generalized ML (p, s, k)-function Wright hypergeometric function Fox H-function Integral transforms |
| url | http://www.sciencedirect.com/science/article/pii/S1110016824015047 |
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