New explicit formulas for the some special matrices with fractional derivatives: II
| Autor: | Xiao-Jun Yang, Yi-Ying Feng, Jian-Gen Liu |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2021 |
| Předmět: |
Caputo fractional derivative
020209 energy 020208 electrical & electronic engineering General Engineering Order (ring theory) Riemann-Liouville fractional derivative 02 engineering and technology Matrix exponential Engineering (General). Civil engineering (General) Fractional calculus Exponential function Matrix (mathematics) Explicit formulas 0202 electrical engineering electronic engineering information engineering Applied mathematics Point (geometry) Statistical analysis TA1-2040 Mathematics |
| Zdroj: | Ain Shams Engineering Journal, Vol 12, Iss 2, Pp 2083-2088 (2021) |
| ISSN: | 2090-4479 |
| Popis: | Matrices have important applications of statistical analysis, circuits, mechanics, optics, and quantum physics. In this article, matrix explicit formulas of the exponentials for computing exp(αA), where A is a special n × n matrix and α is the order of fractional derivative, were obtained. The definitions of the fractional derivative respectively are the Caputo fractional derivative and Riemann-Liouville fractional derivative. Here, we need to point that the new results can be looked as an extended the previous work of the authors. The explicit formulas can help us better to explore deep connotations from natural science. |
| Databáze: | OpenAIRE |
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