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Theory and Modern Applications

Table 4 Comparison between the standard derivative, Caputo fractional derivatives, and Caputo–Fabrizio fractional derivative for \(R(t)\)

From: A mathematical theoretical study of a particular system of Caputo–Fabrizio fractional differential equations for the Rubella disease model

 

t

 

0

1

2

3

4

5

\(D^{\alpha } \) (α = 1)

2.15

18.6573

28.1124

44.8761

69.9672

107.8351

\({}^{c}D^{\alpha }\) (α = 0.95)

2.1511

18.9631

29.6782

47.9246

70.5361

110.1133

\({}^{cf}D^{\alpha }\) (α = 0.95)

2.1731

19.8653

28.9632

45.3197

68.5167

108.3261