Abstract
In this article a symmetry group of scaling transformations is determined for a partial differential equation of fractional order α, containing among particular cases the diffusion equation, the wave equation, and the fractional diffusion-wave equation. For its group-invariant solutions, an ordinary differential equation of fractional order with the new independent variablez = xt − α/2is derived. The derivative then is an Erdelyi–Kober derivative depending on a parameter α. Its complete solution is given in terms of the Wright and the generalized Wright functions.
| Original language | English |
|---|---|
| Pages (from-to) | 81-97 |
| Number of pages | 17 |
| Journal | Journal of Mathematical Analysis and Applications |
| Volume | 227 |
| Issue number | 1 |
| DOIs | |
| Publication status | Published - 1998 |
Fields of science
- 101002 Analysis
- 101029 Mathematical statistics
- 101014 Numerical mathematics
- 101024 Probability theory
- 101015 Operations research
- 101026 Time series analysis
- 101019 Stochastics
- 107 Other Natural Sciences
- 211 Other Technical Sciences
JKU Focus areas
- Computation in Informatics and Mathematics
- Engineering and Natural Sciences (in general)