2019
DOI: 10.1186/s13662-019-2138-9
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Abstract: In recent years, many new definitions of fractional derivatives have been proposed and used to develop mathematical models for a wide variety of real-world systems containing memory, history, or nonlocal effects. The main purpose of the present paper is to develop and analyze a Caputo-Fabrizio fractional derivative model for the HIV/AIDS epidemic which includes an antiretroviral treatment compartment. The existence and uniqueness of the system of solutions of the model are established using a fixed-point theor… Show more

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Cited by 65 publications
(33 citation statements)
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“…A recently published survey-cum-expository review article [11] provides an elementary and introductory overview of fractional calculus for nonprofessional readers. More specifically, the fields of engineering, epidemiology and social sciences have various mathematical modeling applications for mitigating public health risks [12] , [13] , [14] , [15] , [16] , [17] , [18] . In epidemiology, deterministic mathematical models have an important function in investigating the dynamics of infectious diseases.…”
Section: Introductionmentioning
confidence: 99%
“…A recently published survey-cum-expository review article [11] provides an elementary and introductory overview of fractional calculus for nonprofessional readers. More specifically, the fields of engineering, epidemiology and social sciences have various mathematical modeling applications for mitigating public health risks [12] , [13] , [14] , [15] , [16] , [17] , [18] . In epidemiology, deterministic mathematical models have an important function in investigating the dynamics of infectious diseases.…”
Section: Introductionmentioning
confidence: 99%
“…Atangana and Nieto [24] studied the numerical approximation of this new fractional derivative and established an improved RLC circuit model. Moore et al [25] developed and analyzed a Caputo-Fabrizio fractional derivative model for the HIV epidemic which includes an antiretroviral treatment compartment. Dokuyucu et al [26] applied the fractional derivative of Caputo-Fabrizio to model the cancer treatment by radiotherapy.…”
Section: Introductionmentioning
confidence: 99%
“…They also found all exact solutions of this fractionalorder model using the Laplace transform. More recent applications of fractional-order differential equations in biological studies can be found in [25][26][27][28].…”
Section: Introductionmentioning
confidence: 99%