Analysis of the model of HIV-1 infection of $CD4^{+}$ T-cell with a new approach of fractional derivative

Băleanu, Dumitru; Mohammadi, Hakimeh; Rezapour, Shahram

doi:10.1186/s13662-020-02544-w

Cited by 209 publications

(124 citation statements)

References 41 publications

Supporting

Mentioning

124

Contrasting

Order By: Relevance

“…In recent time, some significant work has been produced. The respective work has been carried out to investigate mainly the existence of a solution, or series-type solutions, by using various tools of applied analysis, for details, see [13,[21][22][23]. In an attempt to contribute to the existing literature on mathematical tools to handle similar problems, we propose the use of LADM, which is used to find analytical approximate solution to many nonlinear problems.…”

Section: Bymentioning

confidence: 99%

Fractional dynamical analysis of measles spread model under vaccination corresponding to nonsingular fractional order derivative

et al. 2020

View full text Add to dashboard Cite

In this paper, our main purpose is to present an analytical solution for measles spread model with three doses of vaccination using Caputo-Fabrizio fractional derivative (CFFD). The presented solution is based on Laplace transform with Adomian decomposition method (LADM), which is an effective technique to obtain a solution for such type of problems. Our solution involves nonlinear differential equations of fractional order (FODEs) with non-singular kernel. Also, we provide analysis to verify the existence of a solution to the considered model using fixed point theory. Numerical results are presented to verify the model building analysis, which proved to be efficient in solving such problems.

show abstract

Section: Bymentioning

confidence: 99%

Fractional dynamical analysis of measles spread model under vaccination corresponding to nonsingular fractional order derivative

et al. 2020

View full text Add to dashboard Cite

show abstract

“…Studies on the methods of solving fractional differential equations and the application of fractional systems have also been conducted [18][19][20][21][22][23][24]. In recent years, fractional-order derivatives have expanded and have been widely used in modeling real-world phenomena and investigating the process of disease transmission and control (see, for example, [25][26][27][28][29][30][31][32][33][34][35]). Also, some studies in the biological models with fractional-order derivative have been conducted in recent years [36][37][38][39].…”

Section: Introductionmentioning

confidence: 99%

A new mathematical model for Zika virus transmission

2020

Self Cite

View full text Add to dashboard Cite

We present a new mathematical model for the transmission of Zika virus between humans as well as between humans and mosquitoes. In this way, we use the fractional-order Caputo derivative. The region of the feasibility of system and equilibrium points are calculated, and the stability of equilibrium point is investigated. We prove the existence of a unique solution for the model by using the fixed point theory. By using the fractional Euler method, we get an approximate solution to the model. Numerical results are presented to investigate the effect of fractional derivative on the behavior of functions and also to compare the integer-order derivative and fractional-order derivative results.

show abstract

“…The application can be found in heat transfer in Benard convection, extended irreversible thermodynamics, and shock waves in rigid heat conductors. Many mathematical models like as human immunodeficiency virus (HIV) model, 22 RCL circuit, 23 and steps crisis model of integrodifferential equation, 24,25 Our article is outlined as follows. In Section 2, we discussed Caputo, RL, and C-F fractional derivative.…”

Section: Introductionmentioning

confidence: 99%

Numerical solutions for the reaction–diffusion, diffusion‐wave, and Cattaneo equations using a new operational matrix for the Caputo–Fabrizio derivative

Kumar¹,

Gómez-Aguilar

Pandey³

2020

Math Methods in App Sciences

View full text Add to dashboard Cite

In this research work, we study the model of nonlinear reaction–diffusion equation, diffusion‐wave equation, and Cattaneo equation with the help of a numerical method in which time‐fractional derivative is of Caputo–Fabrizio type (C‐F). First, we derive a formula of the fractional‐order C‐F derivative of xk. Using this formula and some properties of shifted Chebyshev polynomials, we find out the operational matrix of the C‐F derivative. We solve a new class of fractional partial differential equations (FPDEs) using the collocation method and C‐F operational matrix. We depict the feasibility and validity of this numerical method by giving the solution of some numerical examples. We take the diffusion equation, nonlinear reaction–diffusion equation, diffusion‐wave equation, and Cattaneo equation as a particular case of our model. By comparing the obtained numerical results with the given exact solution, we draw an error table depicting that our results are so accurate and desirable accuracy. In the authors' knowledge, the C‐F shifted Chebyshev operational matrix is derived for the first time in this work.

show abstract

Analysis of the model of HIV-1 infection of $CD4^{+}$ T-cell with a new approach of fractional derivative

Cited by 209 publications

References 41 publications

Fractional dynamical analysis of measles spread model under vaccination corresponding to nonsingular fractional order derivative

Fractional dynamical analysis of measles spread model under vaccination corresponding to nonsingular fractional order derivative

A new mathematical model for Zika virus transmission

Numerical solutions for the reaction–diffusion, diffusion‐wave, and Cattaneo equations using a new operational matrix for the Caputo–Fabrizio derivative

Contact Info

Product

Resources

About