# Application of fuzzy ABC fractional differential equations in infectious diseases

Document Type : Research Paper

Authors

1 Department of Mathematics, Faculty of Science, Gonbad Kavous University, Gonbad Kavous, Iran.

2 Faculty of Engineering and Natural Sciences, Istinye University, Istanbul, Tukey.

3 Department of mathematics, Science and research branch, Islamic Azad university, Tehran, Iran.

Abstract

In this paper, for solving the HIV fuzzy mathematical model, it is first transformed into a system of three nonlinear fuzzy Atangana-Baleanu-Caputo (ABC) fractional differential equations with three unknowns and fuzzy initial values. Then, using the generalized Hukuhara difference and ABC fractional derivative and applying the fuzzy numerical ABC-PI method, its fuzzy solution is calculated. Moreover, some theorems are defined to prove the existence and uniqueness of the solution. Then, it is explained that the proposed method can In this paper, for solving the HIV fuzzy mathematical model, it is first transformed into a system of three nonlinear fuzzy Atangana-Baleanu-Caputo (ABC) fractional differential equations with three unknowns and fuzzy initial values. Then, using the generalized Hukuhara difference and ABC fractional derivative and applying the fuzzy numerical ABC-PI method, its fuzzy solution is calculated. Moreover, some theorems are defined to prove the existence and uniqueness of the solution. Then, it is explained that the proposed method can be used for the system of any  equations with  unknowns.  Therefore, in order to determine the solution of the fuzzy mathematical model of the transmission of COVID-19, it is transformed into a system of six nonlinear fuzzy Atangana-Baleanu-Caputo (ABC) fractional differential equations with six unknowns and fuzzy initial values and is solved similarly. At the end, a numerical example is presented to verify the effectiveness of the proposed method.be used for the system of any equations with unknowns. Therefore, in order to determine the solution of the fuzzy mathematical model of the transmission of COVID-19, it is transformed into a system of six nonlinear fuzzy Atangana-Baleanu-Caputo (ABC) fractional differential equations with six unknowns and fuzzy initial values and is solved similarly. At the end, a numerical example is presented to verify the effectiveness of the proposed method.

Keywords 20.1001.1.23453982.2024.12.1.1.8

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### History

• Receive Date: 04 September 2021
• Revise Date: 11 June 2023
• Accept Date: 12 June 2023