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Theory and Modern Applications

Table 1 Results of three types of derivative: ordinary derivative \(D^{\nu }\), Caputo fractional derivative \(^{c}D^{\nu }\), and Caputo–Fabrizio fractional derivative \({}^{\mathrm{CF}}D^{\nu }\) for \(T(t)\)

From: Analysis of the model of HIV-1 infection of \(CD4^{+}\) T-cell with a new approach of fractional derivative

t

0

1

2

3

4

5

\(D^{\nu }\) (ν = 1)

1000

1010

1020

1030

1040

1050

\(^{c}D^{\nu }\) (ν = 0.95)

1000

1007.6

1014.5

1021.4

1028

1034.5

\({}^{\mathrm{CF}}D^{\nu }\) (ν = 0.95)

1000.49999

1009.9999

1019.4998

1028.9996

1038.49909

1047.9983