Fractional differential equations: alpha-entire solutions, regular and irregular singularities
| dc.creator | Kochubei, Anatoly N. | |
| dc.date | 2008-06-11 | |
| dc.date | 2008-11-22 | |
| dc.date.accessioned | 2026-07-07T10:19:50Z | |
| dc.date.available | 2026-07-07T10:19:50Z | |
| dc.description | We consider fractional differential equations of order $α\in (0,1)$ for functions of one independent variable $t\in (0,\infty)$ with the Riemann-Liouville and Caputo-Dzhrbashyan fractional derivatives. A precise estimate for the order of growth of $α$-entire solutions is given. An analog of the Frobenius method for systems with regular singularity is developed. For a model example of an equation with a kind of an irregular singularity, a series for a formal solution is shown to be convergent for $t>0$ (if $α$ is an irrational number poorly approximated by rational ones) but divergent in the distribution sense. | |
| dc.description | 20 pages; to appear in Fractional Calculus and Applied Analysis | |
| dc.identifier | https://arxiv.org/abs/0806.1826 | |
| dc.identifier | http://arxiv.org/abs/0806.1826 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/174655 | |
| dc.subject | Classical Analysis and ODEs | |
| dc.subject | Mathematical Physics | |
| dc.subject | 26A33; 34M99 | |
| dc.title | Fractional differential equations: alpha-entire solutions, regular and irregular singularities | |
| dc.type | text |