| Autor: |
Roscani, Sabrina, Tarzia, Domingo, Venturato, Lucas |
| Rok vydání: |
2018 |
| Předmět: |
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| Druh dokumentu: |
Working Paper |
| Popis: |
This paper deals with the fractional Caputo--Fabrizio derivative and some basic properties related. A computation of this fractional derivative to power functions is given in terms of Mittag--Lefler functions. The inverse operator named the fractional Integral of Caputo--Fabrizio is also analyzed. The main result consists in the proof of existence and uniqueness of a global solution to a nonlinear fractional differential equation, which has been solved previously for short times by Lozada and Nieto (Progr. Fract. Differ. Appl., 1(2):87--92, 2015). The effects of memory as well as the convergence of the obtained results when $\al \nearrow 1$ (and the classical first derivative is recovered) are analyzed throughout the paper. |
| Databáze: |
arXiv |
| Externí odkaz: |
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