A fractional differential equation model for the COVID-19 transmission by using the Caputo–Fabrizio derivative

A fractional differential equation model for the COVID-19 transmission by using the Caputo–Fabrizio derivative

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 seri...

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Bibliographic Details
Main Authors: Dumitru Baleanu, Hakimeh Mohammadi, Shahram Rezapour
Format: Article
Language:English
Published: SpringerOpen 2020-06-01
Series:Advances in Difference Equations
Subjects:
Fixed point
Homotopy analysis method
Mathematical model
Numerical simulation
Caputo–Fabrizio derivative
Online Access:http://link.springer.com/article/10.1186/s13662-020-02762-2
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spelling doaj-0f47e532b2ec4c9c8b8edbfc83c97fde2020-11-25T02:58:42ZengSpringerOpenAdvances in Difference Equations1687-18472020-06-012020112710.1186/s13662-020-02762-2A fractional differential equation model for the COVID-19 transmission by using the Caputo–Fabrizio derivativeDumitru Baleanu0Hakimeh Mohammadi1Shahram Rezapour2Department of Mathematics, Cankaya UniversityDepartment of Mathematics, Miandoab Branch, Islamic Azad UniversityDepartment of Mathematics, Azarbaijan Shahid Madani UniversityAbstract 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.http://link.springer.com/article/10.1186/s13662-020-02762-2Fixed pointHomotopy analysis methodMathematical modelNumerical simulationCaputo–Fabrizio derivative
collection DOAJ
language English
format Article
sources DOAJ
author Dumitru Baleanu
Hakimeh Mohammadi
Shahram Rezapour
spellingShingle Dumitru Baleanu
Hakimeh Mohammadi
Shahram Rezapour
A fractional differential equation model for the COVID-19 transmission by using the Caputo–Fabrizio derivative
Advances in Difference Equations
Fixed point
Homotopy analysis method
Mathematical model
Numerical simulation
Caputo–Fabrizio derivative
author_facet Dumitru Baleanu
Hakimeh Mohammadi
Shahram Rezapour
author_sort Dumitru Baleanu
title A fractional differential equation model for the COVID-19 transmission by using the Caputo–Fabrizio derivative
title_short A fractional differential equation model for the COVID-19 transmission by using the Caputo–Fabrizio derivative
title_full A fractional differential equation model for the COVID-19 transmission by using the Caputo–Fabrizio derivative
title_fullStr A fractional differential equation model for the COVID-19 transmission by using the Caputo–Fabrizio derivative
title_full_unstemmed A fractional differential equation model for the COVID-19 transmission by using the Caputo–Fabrizio derivative
title_sort fractional differential equation model for the covid-19 transmission by using the caputo–fabrizio derivative
publisher SpringerOpen
series Advances in Difference Equations
issn 1687-1847
publishDate 2020-06-01
description 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.
topic Fixed point
Homotopy analysis method
Mathematical model
Numerical simulation
Caputo–Fabrizio derivative
url http://link.springer.com/article/10.1186/s13662-020-02762-2
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