A mathematical theoretical study of a particular system of Caputo–Fabrizio fractional differential equations for the Rubella disease model

Published on Dec 1, 2020in Advances in Difference Equations2.803
· DOI :10.1186/S13662-020-02614-Z
Dumitru Baleanu106
Estimated H-index: 106
(China Medical University (Taiwan)),
Hakimeh Mohammadi15
Estimated H-index: 15
(IAU: Islamic Azad University),
Shahram Rezapour31
Estimated H-index: 31
(Azarbaijan Shahid Madani University)
Sources
Abstract
In this paper, we study the rubella disease model with the Caputo–Fabrizio fractional derivative. The mathematical solution of the liver model is presented by a three-step Adams–Bashforth scheme. The existence and uniqueness of the solution are discussed by employing fixed point theory. Finally some numerical simulations are showed to underpin the effectiveness of the used derivative.
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#2Hakimeh Mohammadi (IAU: Islamic Azad University)H-Index: 15
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By using the fractional Caputo–Fabrizio derivative, we investigate a new version for the mathematical model of HIV. In this way, we review the existence and uniqueness of the solution for the model by using fixed point theory. We solve the equation by a combination of the Laplace transform and homotopy analysis method. Finally, we provide some numerical analytics and comparisons of the results.
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In this paper, the transient response of the parallel RCL circuit with Caputo–Fabrizio derivative is solved by Laplace transforms. Also, the graphs of the obtained solutions for the different orders of the fractional derivatives are compared with each other and with the usual solutions. Finally, they are compared with practical and laboratory results.
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Abstract In this research, we aim to propose a new fractional model for human liver involving Caputo–Fabrizio derivative with the exponential kernel. Concerning the new model, the existence of a unique solution is explored by using the Picard–Lindelof approach and the fixed-point theory. In addition, the mathematical model is implemented by the homotopy analysis transform method whose convergence is also investigated. Eventually, numerical experiments are carried out to better illustrate the res...
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In this paper, stability analysis of a fractional-order linear system described by the Caputo–Fabrizio (CF) derivative is studied. In order to solve the problem, character equation of the system is defined at first by using the Laplace transform. Then, some simple necessary and sufficient stability conditions and sufficient stability conditions are given which will be the basis of doing research of a fractional-order system with a CF derivative. In addition, the difference of stability domain be...
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We extend the fractional Caputo–Fabrizio derivative of order \(0\leq \sigma <1\) on \(C_{\mathbb{R}}[0,1]\) and investigate two higher-order series-type fractional differential equations involving the extended derivation. Also, we provide an example to illustrate one of the main results.
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