Theory and Modern Applications
Table 3 Comparison between standard derivative, Caputo fractional derivatives and Caputo-Fabrizio fractional derivative for the heavy smokers \(\pmb{S(t)}\)
t | Standard derivative ( ρ = 1) | Caputo derivative ( ρ = 0.95) | Caputo-Fabrizio derivative ( ρ = 0.95) |
|---|---|---|---|
1 | 0.1026239640 | 0.1025641835 | 0.1026437765 |
2 | 0.09937450414 | 0.09948799415 | 0.09956153608 |
3 | 0.09646354464 | 0.09680263691 | 0.09678199000 |
4 | 0.09382300970 | 0.09440789173 | 0.09424677174 |
5 | 0.09138482355 | 0.09222574223 | 0.09189751483 |