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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| Main Authors: | , , , , , , |
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| Format: | Article |
| Language: | English |
| Published: |
Elsevier
2025-02-01
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| Series: | Alexandria Engineering Journal |
| Subjects: | |
| Online Access: | http://www.sciencedirect.com/science/article/pii/S1110016824015047 |
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| Summary: | 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. |
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| ISSN: | 1110-0168 |