On the mathematical model of Rabies by using the fractional Caputo–Fabrizio derivative

Seher Melike Aydogan; Dumitru Baleanu; Hakimeh Mohammadi; Shahram Rezapour

doi:10.1186/s13662-020-02798-4

On the mathematical model of Rabies by using the fractional Caputo–Fabrizio derivative

Seher Melike Aydogan
, Dumitru Baleanu
, Hakimeh Mohammadi
, Shahram Rezapour^*

^*Corresponding author for this work

Department of Mathematics Engineering

Cankaya University
Institute for Space Sciences
Islamic Azad University
Duy Tan University
China Medical University Taichung

Research output: Contribution to journal › Article › peer-review

76 Citations (Scopus)

Abstract

Using the fractional Caputo–Fabrizio derivative, we investigate a new version of the mathematical model of Rabies disease. Using fixed point results, we prove the existence of a unique solution. We calculate the equilibrium points and check the stability of solutions. We solve the equation by combining the Laplace transform and Adomian decomposition method. In numerical results, we investigate the effect of coefficients on the number of infected groups. We also examine the effect of derivation orders on the behavior of functions and make a comparison between the results of the integer-order derivative and the Caputo and Caputo–Fabrizio fractional-order derivatives.

Original language	English
Article number	382
Journal	Advances in Difference Equations
Volume	2020
Issue number	1
DOIs	https://doi.org/10.1186/s13662-020-02798-4
Publication status	Published - 1 Dec 2020

Bibliographical note

Publisher Copyright:
© 2020, The Author(s).

Funding

Research of the fourth author was supported by Azarbaijan Shahid Madani University. Also, research of the third author was supported by Miandoab Branch, Islamic Azad University. The authors are thankful to dear referees for their valuable comments which basically improved the final version of this work.

Funders
Islamic Azad University
Azarbaijan Shahid Madani University

UN SDGs

This output contributes to the following UN Sustainable Development Goals (SDGs)

SDG 3 Good Health and Well-being

Keywords

Adomian decomposition method
Fixed point
Numerical simulation
Rabies model
The Caputo–Fabrizio fractional derivative

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10.1186/s13662-020-02798-4

Cite this

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abstract = "Using the fractional Caputo–Fabrizio derivative, we investigate a new version of the mathematical model of Rabies disease. Using fixed point results, we prove the existence of a unique solution. We calculate the equilibrium points and check the stability of solutions. We solve the equation by combining the Laplace transform and Adomian decomposition method. In numerical results, we investigate the effect of coefficients on the number of infected groups. We also examine the effect of derivation orders on the behavior of functions and make a comparison between the results of the integer-order derivative and the Caputo and Caputo–Fabrizio fractional-order derivatives.",

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AU - Baleanu, Dumitru

AU - Mohammadi, Hakimeh

AU - Rezapour, Shahram

PY - 2020/12/1

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N2 - Using the fractional Caputo–Fabrizio derivative, we investigate a new version of the mathematical model of Rabies disease. Using fixed point results, we prove the existence of a unique solution. We calculate the equilibrium points and check the stability of solutions. We solve the equation by combining the Laplace transform and Adomian decomposition method. In numerical results, we investigate the effect of coefficients on the number of infected groups. We also examine the effect of derivation orders on the behavior of functions and make a comparison between the results of the integer-order derivative and the Caputo and Caputo–Fabrizio fractional-order derivatives.

AB - Using the fractional Caputo–Fabrizio derivative, we investigate a new version of the mathematical model of Rabies disease. Using fixed point results, we prove the existence of a unique solution. We calculate the equilibrium points and check the stability of solutions. We solve the equation by combining the Laplace transform and Adomian decomposition method. In numerical results, we investigate the effect of coefficients on the number of infected groups. We also examine the effect of derivation orders on the behavior of functions and make a comparison between the results of the integer-order derivative and the Caputo and Caputo–Fabrizio fractional-order derivatives.

KW - Adomian decomposition method

KW - Fixed point

KW - Numerical simulation

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KW - The Caputo–Fabrizio fractional derivative

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VL - 2020

JO - Advances in Difference Equations

JF - Advances in Difference Equations

IS - 1

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ER -

On the mathematical model of Rabies by using the fractional Caputo–Fabrizio derivative

Abstract

Bibliographical note

Funding

UN SDGs

Keywords

Access to Document

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