Green's Function Framework for Boundary Value Problems with the Regularized Prabhakar Fractional Derivative
Fuente:
arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2026
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| _version_ | 1866910244338139136 |
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| author | Karimov, Erkinjon Usmonov, Doniyor Mirzaeva, Maftuna |
| author_facet | Karimov, Erkinjon Usmonov, Doniyor Mirzaeva, Maftuna |
| contents | In this work, the first initial-boundary value problem for a sub-diffusion equation involving the regularized Prabhakar fractional derivative is studied. The problem is solved by reducing it to two initial-boundary value problems using the superposition method. An explicit representation of the solution and the corresponding Green's function is obtained. The explicit form of the Green's function is expressed in terms of a bivariate Mittag-Leffler type function. Then, it is proved that the obtained solution indeed constitutes the solution of the considered problem. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_24252 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Green's Function Framework for Boundary Value Problems with the Regularized Prabhakar Fractional Derivative Karimov, Erkinjon Usmonov, Doniyor Mirzaeva, Maftuna Analysis of PDEs 35R11 F.2.2 In this work, the first initial-boundary value problem for a sub-diffusion equation involving the regularized Prabhakar fractional derivative is studied. The problem is solved by reducing it to two initial-boundary value problems using the superposition method. An explicit representation of the solution and the corresponding Green's function is obtained. The explicit form of the Green's function is expressed in terms of a bivariate Mittag-Leffler type function. Then, it is proved that the obtained solution indeed constitutes the solution of the considered problem. |
| title | Green's Function Framework for Boundary Value Problems with the Regularized Prabhakar Fractional Derivative |
| topic | Analysis of PDEs 35R11 F.2.2 |
| url | https://arxiv.org/abs/2603.24252 |