Green's Function and Solution Representation for a Boundary Value Problem Involving the Prabhakar Fractional Derivative
Fuente:
arXiv
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866914579882180608 |
|---|---|
| author | Karimov, Erkinjon Usmonov, Doniyor Mirzaeva, Maftuna |
| author_facet | Karimov, Erkinjon Usmonov, Doniyor Mirzaeva, Maftuna |
| contents | We investigate a first boundary value problem for a second-order partial differential equation involving the Prabhakar fractional derivative in time. Using structural properties of the Prabhakar kernel and generalized Mittag-Leffler functions, we reduce the problem to a Volterra-type integral equation. This reduction enables the explicit construction of the corresponding Green's function. Based on the obtained Green's function, we derive a closed-form integral representation of the solution and prove its existence and uniqueness. The results extend classical Green-function techniques to a wider class of fractional operators and provide analytical tools for further study of boundary and inverse problems associated with Prabhakar-type fractional differential equations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_21259 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Green's Function and Solution Representation for a Boundary Value Problem Involving the Prabhakar Fractional Derivative Karimov, Erkinjon Usmonov, Doniyor Mirzaeva, Maftuna Analysis of PDEs Mathematical Physics 35R11 We investigate a first boundary value problem for a second-order partial differential equation involving the Prabhakar fractional derivative in time. Using structural properties of the Prabhakar kernel and generalized Mittag-Leffler functions, we reduce the problem to a Volterra-type integral equation. This reduction enables the explicit construction of the corresponding Green's function. Based on the obtained Green's function, we derive a closed-form integral representation of the solution and prove its existence and uniqueness. The results extend classical Green-function techniques to a wider class of fractional operators and provide analytical tools for further study of boundary and inverse problems associated with Prabhakar-type fractional differential equations. |
| title | Green's Function and Solution Representation for a Boundary Value Problem Involving the Prabhakar Fractional Derivative |
| topic | Analysis of PDEs Mathematical Physics 35R11 |
| url | https://arxiv.org/abs/2512.21259 |