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Theory and Modern Applications

Table 2 Comparison between the standard derivative, Caputo fractional derivatives, and Caputo–Fabrizio fractional derivative for \(E(t)\)

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)

9.5612

12.0014

9.1120

6.021

3.998

2.8791

\({}^{c}D^{\alpha }\) (α = 0.95)

9.8721

13.9864

10.2341

7.234

4.5432

3.5402

\({}^{cf}D^{\alpha }\) (α = 0.95)

10.5704

13.0185

9.9593

6.7502

4.4770

3.0694