%0 Journal Article
%T Application of fuzzy ABC fractional differential equations in infectious diseases
%J Computational Methods for Differential Equations
%I University of Tabriz
%Z 2345-3982
%A Babakordi, Fatemeh
%A Allahviranloo, Tofigh
%D 2024
%\ 11/01/2024
%V 12
%N 1
%P 1-15
%! Application of fuzzy ABC fractional differential equations in infectious diseases
%K Fuzzy Atangana-Baleanu-Caputo(ABC) fractional derivative
%K Fuzzy ABC fractional differential equations
%K HIV fuzzy mathematical model
%R 10.22034/cmde.2023.47768.2000
%X 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.
%U https://cmde.tabrizu.ac.ir/article_16440_5dc73843d9a4cf0bdafdc6d06ccb4647.pdf