Interactive Fuzzy Fractional Differential Equation: Application on HIV Dynamics

Wasques, Vinícius Francisco; Laiate, Beatriz; Pedro, Francielle Santo; Esmi, Estevão; Barros, Laécio Carvalho de

doi:10.1007/978-3-030-50153-2_15

Cited by 9 publications

(4 citation statements)

References 30 publications

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“…The concept of fuzzy linear correlation suggests the existence of a memory in the fuzzy process. Biological processes were already described as autocorrelated fuzzy processes or, specifically, as linearly correlated processes, in a wide range of papers [11,21,28,29,31,32]. There are two cases to consider: the case where λ ∈ R, and the case where λ ∈ R F (A) \R.…”

Section: The Hutchinson Equationmentioning

confidence: 99%

A-Cross Product for Autocorrelated Fuzzy Processes: The Hutchinson Equation

Longo

Laiate

Pedro

et al. 2021

Lecture Notes in Networks and Systems

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This paper presents a new operation of multiplication between linearly correlated fuzzy numbers based on the concept of cross product, set for fuzzy numbers in general. It is proved that this operation is closed in the set of linearly correlated fuzzy numbers. Some properties of the multiplication are listed, and an application on the delayed logistic model, the Hutchinson equation, is provided when considering the population an autocorrelated fuzzy process. Lastly, an analysis of the stability of the solution and biological interpretations are established.

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Section: The Hutchinson Equationmentioning

confidence: 99%

A-Cross Product for Autocorrelated Fuzzy Processes: The Hutchinson Equation

Longo

Laiate

Pedro

et al. 2021

Lecture Notes in Networks and Systems

Self Cite

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“…To get an approximation of the solution to fuzzy fractional calculus models, many sophisticated methods such as Euler method [25], Laplace transform method [26], residual power series method [27], and homotopy analysis method [28] have been developed. For instance, Zambrano-Serrano et al [29] and Wasques et al [30] perused how fuzzy fractional calculus might be applied in the context of chaotic dynamics and HIV dynamics, respectively. Additionally, many FFDEs approaches using Pythagorean fuzzy sets are described [31,32].…”

Section: Introductionmentioning

confidence: 99%

Numerical solution of fuzzy fractional volterra integro differential equations with boundary conditions

Agilan,

Parthiban

2024

Phys. Scr.

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In this study, the boundary value problem of fuzzy fractional nonlinear Volterra integro differential equations of order 1 < ρ ≤ 2 is addressed. Fuzzy fractional derivatives are defined in the Caputo sense. To show the existence result, the Krasnoselkii theorem from the theory of fixed points is used, where as the well-known contraction mapping concept is utilized in order to show the solution is unique to the proposed problem. Moreover, a novel Adomian decomposition method is utilized to get numerical solution; the approach behind deriving the solution is from Adomian polynomials, and it is organized according to the recursive relation that is obtained. The proposed method significantly decreases the numerical computations by obtaining solutions without the need of discretization or constrictive assumptions. According to the results, there is substantial agreement between the seriessolutions produced by the fuzzy Adomian decomposition method. Finally, using MATLAB, the symmetry between the lower and upper-cut representations of the fuzzy solutions is demonstrated in the numerical result.

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“…The current issue and full text archive of this journal is available on Emerald Insight at: https://www.emerald.com/insight/0264-4401.htm (Liang et al, 2018), inverse fractional advection-dispersion problem (Lobato et al, 2019), anomalous diffusion equations (Yang et al, 2019), risk theory (Constantinescu et al, 2019), HIV dynamics (Wasques et al, 2020), solution of mathematical equations using spline collocation methods (Zahra et al, 2020) and Langevin equation (Yang et al, 2020).…”

Section: Introductionmentioning

confidence: 99%

“…In the past decades, different applications considering models represented by fractional order in different fields of science have been published in the literature. Among them, we can cite studies on chemistry (Kirchner et al , 2000), finance (Sabatelli et al , 2002; Bohner and Hatipoğlu, 2018, 2019), hydrology (Schumer et al , 2003), biology (Magin, 2006), viscoelasticity (Larsson et al , 2015), eigenvalue problem (Jin and Liu, 2016), robotics (Kumar and Rana, 2017), anomalous diffusion (Zhang et al , 2017), anomalous heat-diffusion problems (Yang et al , 2017a), advection-dispersion problems (Yuan et al , 2016; Zhang, 2018; Li and Rui, 2018), fractional Boussinesq equation (Yang et al , 2017b), diffusion equations (Yang et al , 2018; Shi et al , 2020), chaos synchronization (Su et al , 2018), anomalous advection-dispersion equations (Liang et al , 2018), inverse fractional advection-dispersion problem (Lobato et al , 2019), anomalous diffusion equations (Yang et al , 2019), risk theory (Constantinescu et al , 2019), HIV dynamics (Wasques et al , 2020), solution of mathematical equations using spline collocation methods (Zahra et al , 2020) and Langevin equation (Yang et al , 2020).…”

Section: Introductionmentioning

confidence: 99%

Solution of mass-spring-damper fractional systems using Caputo derivative and orthogonal collocation

Lima

Lobato

Steffen

2021

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PurposeIn this contribution, the solution of Mass-Spring-Damper Systems in the fractional context by using Caputo derivative and Orthogonal Collocation Method is investigated. For this purpose, different case studies considering constant and periodic sources are evaluated. The dimensional consistency of the model is guaranteed by introducing an auxiliary parameter. The obtained results are compared with those found by using both the analytical solution and the predictor-corrector method of Adams–Bashforth–Moulton type. The influence of the fractional order on the mechanical system is evaluated.Design/methodology/approachIn the present contribution, an extension of the Orthogonal Collocation Method to solve fractional differential equations is proposed.FindingsIn general, the proposed methodology was able to solve a classical mechanical engineering problem with different characteristics.Originality/valueThe development of a new numerical method to solve fractional differential equations is the major contribution.

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Interactive Fuzzy Fractional Differential Equation: Application on HIV Dynamics

Cited by 9 publications

References 30 publications

A-Cross Product for Autocorrelated Fuzzy Processes: The Hutchinson Equation

A-Cross Product for Autocorrelated Fuzzy Processes: The Hutchinson Equation

Numerical solution of fuzzy fractional volterra integro differential equations with boundary conditions

Solution of mass-spring-damper fractional systems using Caputo derivative and orthogonal collocation

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