Fractional differ-integral involving bicomplex Prabhakar function in the kernel and applications
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arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866908871552925696 |
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| author | Sharma, Urvashi Purohit Agarwal, Ritu |
| author_facet | Sharma, Urvashi Purohit Agarwal, Ritu |
| contents | This paper introduces the bicomplex Prabhakar derivative, extending fractional calculus to four-dimensional bicomplex spaces. Using the generalized kernel involving bicomplex Prabhakar function, we construct the bicomplex Prabhakar derivative and prove fundamental operational properties including linearity, composition rules, and connections to Riemann-Liouville and Caputo operators. We further investigate how fractional operators act on the bicomplex Prabhakar function itself, developing integral representations and transformation formulas.
This work provides a rigorous foundation for modeling complex phenomena with memory effects and multi-dimensional coupling in bicomplex domains. The rich algebraic structure of bicomplex numbers, combined with the flexibility of Prabhakar kernels, offers a versatile framework applicable across diverse scientific and engineering disciplines. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_07034 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Fractional differ-integral involving bicomplex Prabhakar function in the kernel and applications Sharma, Urvashi Purohit Agarwal, Ritu Complex Variables 33E12, 30G35, 26A33, 34A08 This paper introduces the bicomplex Prabhakar derivative, extending fractional calculus to four-dimensional bicomplex spaces. Using the generalized kernel involving bicomplex Prabhakar function, we construct the bicomplex Prabhakar derivative and prove fundamental operational properties including linearity, composition rules, and connections to Riemann-Liouville and Caputo operators. We further investigate how fractional operators act on the bicomplex Prabhakar function itself, developing integral representations and transformation formulas. This work provides a rigorous foundation for modeling complex phenomena with memory effects and multi-dimensional coupling in bicomplex domains. The rich algebraic structure of bicomplex numbers, combined with the flexibility of Prabhakar kernels, offers a versatile framework applicable across diverse scientific and engineering disciplines. |
| title | Fractional differ-integral involving bicomplex Prabhakar function in the kernel and applications |
| topic | Complex Variables 33E12, 30G35, 26A33, 34A08 |
| url | https://arxiv.org/abs/2603.07034 |