Figure 1

The dynamic evolution of system (21) when \(\nu =0.5\), with the approximate solution by fractional Chebyshev polynomials \((\varphi _{2},\psi _{2})= (\frac{2(t+2t^{2})}{\pi }, \frac{2(t+2t^{2})}{\pi })\) for Spain and for Italy with different coefficients \(C_{0.5,2} \). China statistics in March has steady circulation; consequently, we propose \((\varphi _{1},\psi _{1})= (\frac{2t+2}{\pi },\frac{2t+2}{\pi })\). For USA data, the chart shows high rising confirmed cases, therefore we apply exponential connections \(\varphi _{1}(t)(\exp (\sqrt{\varphi _{1}(t)})-1)\) similarly for \(\psi (t)\). Note that the data are shown in March