Operational Calculus for the nth-Level Prabhakar Type Fractional Derivative with Applications
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866918263393353728 |
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| author | Waheed, Imtiaz Karimov, Erkinjon Rehman, Mujeeb ur |
| author_facet | Waheed, Imtiaz Karimov, Erkinjon Rehman, Mujeeb ur |
| contents | This study investigates the nth-level Prabhakar fractional derivative, a generalization encompassing some well-known fractional derivatives. We establish its fundamental properties, particularly its relationship with the corresponding Prabhakar fractional integral. Furthermore, we develop Mikusinski-type operational calculus for this derivative, providing a framework for solving differential equations involving this operator. To illustrate its application, we present analytical solutions of two problems: a fractional order ordinary differential equation and the time fractional heat equation, both of which include the nth-level Prabhakar derivative. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_21273 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Operational Calculus for the nth-Level Prabhakar Type Fractional Derivative with Applications Waheed, Imtiaz Karimov, Erkinjon Rehman, Mujeeb ur Analysis of PDEs 44A40 G.0 This study investigates the nth-level Prabhakar fractional derivative, a generalization encompassing some well-known fractional derivatives. We establish its fundamental properties, particularly its relationship with the corresponding Prabhakar fractional integral. Furthermore, we develop Mikusinski-type operational calculus for this derivative, providing a framework for solving differential equations involving this operator. To illustrate its application, we present analytical solutions of two problems: a fractional order ordinary differential equation and the time fractional heat equation, both of which include the nth-level Prabhakar derivative. |
| title | Operational Calculus for the nth-Level Prabhakar Type Fractional Derivative with Applications |
| topic | Analysis of PDEs 44A40 G.0 |
| url | https://arxiv.org/abs/2512.21273 |