Solution of the SIR epidemic model of arbitrary orders containing Caputo-Fabrizio, Atangana-Baleanu and Caputo derivatives
The main aim of this study was to apply an analytical method to solve a nonlinear system of
fractional differential equations (FDEs). This method is the Adomian decomposition method (ADM),
and a comparison between its results was made by using a numerical method: Runge-Kutta 4 (RK4). It
is proven that there is a unique solution to the system. The convergence of the series solution is given,
and the error estimate is also proven. After that, the susceptible-infected-recovered (SIR) model was
taken as an real phenomenon with such systems. This system is discussed with three different fractional
derivatives (FDs): the Caputo-Fabrizio derivative (CFD), the Atangana-Baleanu derivative (ABD), and
the Caputo derivative (CD). A comparison between these three different derivatives is given. We aimed
to see which one of the new definitions (ABD and CFD) is close to one of the most important classical
definitions (CD).
The main aim of this study was to apply an analytical method to solve a nonlinear system of
fractional differential equations (FDEs). This method is the Adomian decomposition method (ADM),…
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