Higher-order fractional equations and related time-changed pseudo-processes
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866929588148371456 |
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| author | Cinque, Fabrizio Orsingher, Enzo |
| author_facet | Cinque, Fabrizio Orsingher, Enzo |
| contents | We study Cauchy problems of fractional differential equations in both space and time variables by expressing the solution in terms of ``stochastic composition" of the solutions to two simpler problems. These Cauchy sub-problems respectively concern the space and the time differential operator involved in the main equation. We provide some probabilistic and pseudo-probabilistic applications, where the solution can be interpreted as the pseudo-transition density of a time-changed pseudo-process. To extend our results to higher order time-fractional problems, we introduce pseudo-subordinators as well as its pseudo-inverse. Finally, we present our results in the case of more general differential operators and we interpret the results by means of a linear combination of pseudo-subordinators and its inverse. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_13691 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Higher-order fractional equations and related time-changed pseudo-processes Cinque, Fabrizio Orsingher, Enzo Probability 35R11, 60K99 We study Cauchy problems of fractional differential equations in both space and time variables by expressing the solution in terms of ``stochastic composition" of the solutions to two simpler problems. These Cauchy sub-problems respectively concern the space and the time differential operator involved in the main equation. We provide some probabilistic and pseudo-probabilistic applications, where the solution can be interpreted as the pseudo-transition density of a time-changed pseudo-process. To extend our results to higher order time-fractional problems, we introduce pseudo-subordinators as well as its pseudo-inverse. Finally, we present our results in the case of more general differential operators and we interpret the results by means of a linear combination of pseudo-subordinators and its inverse. |
| title | Higher-order fractional equations and related time-changed pseudo-processes |
| topic | Probability 35R11, 60K99 |
| url | https://arxiv.org/abs/2402.13691 |