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Theory and Modern Applications

Table 3 Comparison between the standard derivative, Caputo fractional derivatives, and Caputo–Fabrizio fractional derivative for \(I(t)\)

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)

8.6753

7.84

6.3251

3.987

3.001

2.765

\({}^{c}D^{\alpha }\) (α = 0.95)

8.9674

7.983

5.372

3.865

2.0216

3.2157

\({}^{cf}D^{\alpha }\) (α = 0.95)

9.6789

7.6784

5.934

3.213

2.8764

2.1451