Approximate solutions of one-dimensional systems with fractional derivative

Ferrari, Alberto J.; Gadella, M.; Lara, Luis; Marcus, Eduardo Santillan

doi:10.1142/s0129183120500928

Cited by 2 publications

(3 citation statements)

References 18 publications

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“…Considering the definition of the Caputo derivative, the following approximation is obtained in Ferrari et al [8,10]:…”

Section: Numerical Schemes Consideredmentioning

confidence: 99%

Comparative Study of Some Numerical Schemes for a Fractional Order Model of HIV Infection Treatment

Ferrari¹,

Lara²,

Olguin³

et al. 2022

TCAM

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A fractional order mathematical model that already exists in the literature, was considered. This model was established to study the effects of medicinal treatment in people infected with the human immunodeficiency virus (HIV). The importance of this study is that the model evaluates, among other parameters, the density of healthy and HIV-infected CD4+ T cells. These data are very necessary for the subject infected by the virus given the effects that an antiretroviral treatment causes in it. The objective of this work is to consider several numerical schemes that involve fractional derivatives in order to compare their behaviors and to obtain a good approximation of the mentioned model solution. Convergence of these schemes will be studied as well as sensitivity with respect to the variation of the parameters η (drug efficacy) and α (fractional derivative order). Furthermore, through the collection of medical records of people living with HIV, it is intended to determine the optimal fractional derivative order for the model and to compare it with the classical model.

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“…Considering the definition of the Caputo derivative, the following approximation is obtained in Ferrari et al [8,10]:…”

Section: Numerical Schemes Consideredmentioning

confidence: 99%

Comparative Study of Some Numerical Schemes for a Fractional Order Model of HIV Infection Treatment

Ferrari¹,

Lara²,

Olguin³

et al. 2022

TCAM

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Section: Introductionmentioning

confidence: 99%

“…Fractional calculus is very useful and widely used in many applications in science, numerical computations and engineering, where the mathematical modeling of several real world problems is presented in terms of fractional differential equations, see, e.g., [1][2][3][4][5][6][7][8]. For example, the authors in [8] approximated the Caputo fractional derivative by quadratic segmentary interpolation. That raised a new approach of approximating fractional derivatives and provides some insights for a new applications where the numerical resolution of ordinary fractional differential equations is achieved.…”

Section: Introductionmentioning

confidence: 99%

A Novel Numerical Method for Solving Fractional Diffusion-Wave and Nonlinear Fredholm and Volterra Integral Equations with Zero Absolute Error

Mohammad

Trounev

Alshbool

2021

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In this work, a new numerical method for the fractional diffusion-wave equation and nonlinear Fredholm and Volterra integro-differential equations is proposed. The method is based on Euler wavelet approximation and matrix inversion of an M×M collocation points. The proposed equations are presented based on Caputo fractional derivative where we reduce the resulting system to a system of algebraic equations by implementing the Gaussian quadrature discretization. The reduced system is generated via the truncated Euler wavelet expansion. Several examples with known exact solutions have been solved with zero absolute error. This method is also applied to the Fredholm and Volterra nonlinear integral equations and achieves the desired absolute error of 0×10−31 for all tested examples. The new numerical scheme is exceptional in terms of its novelty, efficiency and accuracy in the field of numerical approximation.

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Approximate solutions of one-dimensional systems with fractional derivative

Cited by 2 publications

References 18 publications

Comparative Study of Some Numerical Schemes for a Fractional Order Model of HIV Infection Treatment

Comparative Study of Some Numerical Schemes for a Fractional Order Model of HIV Infection Treatment

A Novel Numerical Method for Solving Fractional Diffusion-Wave and Nonlinear Fredholm and Volterra Integral Equations with Zero Absolute Error

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