Bicomplex <i>k</i>-Mittag-Leffler Functions with Two Parameters: Theory and Applications to Fractional Kinetic Equations
In this paper, we aim to extend the bicomplex two-parameter Mittag-Leffler (M-L) function by introducing a new <i>k</i>-parameter. This results in the definition of the bicomplex <i>k</i>-M-L function with two parameters. This generalization offers more flexibility and broade...
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| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2025-05-01
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| Series: | Fractal and Fractional |
| Subjects: | |
| Online Access: | https://www.mdpi.com/2504-3110/9/6/344 |
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| Summary: | In this paper, we aim to extend the bicomplex two-parameter Mittag-Leffler (M-L) function by introducing a new <i>k</i>-parameter. This results in the definition of the bicomplex <i>k</i>-M-L function with two parameters. This generalization offers more flexibility and broader applicability in modeling complex fractional systems. We explore its key properties, develop new theorems, and establish the corresponding <i>k</i>-Riemann–Liouville fractional calculus within the bicomplex setting for the extended function. Furthermore, we solve several fractional differential equations using the bicomplex <i>k</i>-M-L function with two parameters. The results prove the enhanced flexibility and generality of the proposed function, particularly in deriving fractional kinetic equations, offering novel insights beyond existing bicomplex fractional models. |
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| ISSN: | 2504-3110 |