A fractional differential equation model for the COVID-19 transmission by using the Caputo–Fabrizio derivative
Dumitru Bǎleanu, Hakimeh Mohammadi, Shahram Rezapour
Abstract
We present a fractional-order model for the COVID-19 transmission with Caputo-Fabrizio derivative. Using the homotopy analysis transform method (HATM), which combines the method of homotopy analysis and Laplace transform, we solve the problem and give approximate solution in convergent series. We prove the existence of a unique solution and the stability of the iteration approach by using fixed point theory. We also present numerical results to simulate virus transmission and compare the results with those of the Caputo derivative.
Topics & Concepts
MathematicsHomotopy analysis methodFractional calculusLaplace transformPartial differential equationHomotopyOrdinary differential equationApplied mathematicsDerivative (finance)Mathematical analysisDifferential equationPure mathematicsEconomicsFinancial economicsFractional Differential Equations SolutionsIterative Methods for Nonlinear EquationsAdvanced Control Systems Design