Fréchet derivative for linearly correlated fuzzy function

Esmi, Estevão; Pedro, Francielle Santo; Barros, Laécio Carvalho de; Lodwick, Weldon A.

doi:10.1016/j.ins.2017.12.051

Cited by 61 publications

(30 citation statements)

References 13 publications

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“…The multiplicity of solutions related to so-called switching points forcing us to solve two different equations at the same time. On the other hand, to enrich the field of research some other contributions were also investigated by Chalco-Cano et al (2009) (under the name of π-derivatives), and more recently by Esmi et al (2018) (Fréchet derivatives) and by (granular derivatives).…”

Section: A Brief Review On the Differentiability Of Fuzzy-valued Funcmentioning

confidence: 99%

Fuzzy delay differential equations under granular differentiability with applications

Son¹,

Long

Dong

2019

Comp. Appl. Math.

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In this paper, we consider a new setting of fuzzy delay differential equations by employing the concepts of granular differentiability. Firstly, we establish some basic properties of complete granular metric space. Then we study the local and global existence and uniqueness of integral fuzzy solution. For the first task, we use successive approximation technique combined with Gronwall's lemma. The second task will be solved by Banach contraction principle in weighted metric space defined by granular distance. Additionally, we demonstrate the theoretical results by solving some real-world models in both analytical method and numerical method. The first model is often referred to the exponential growth, namely time-delay growth Malthusian model. The second model is one type of dynamical systems, which is used for studies involving large amounts of tissues, called Ehrlich ascites tumor model with delay. Furthermore, we introduce the Mackey-Glass model which is considered as a useful tool for times series prediction in the neutral network and fuzzy logic fields. Finally, we represent the surface of fuzzy solution for visible identification mark-on. Keywords Granular differentiability • Fuzzy delay differential equations • Malthusian growth model • Ehrlich ascites tumor model • Mackey-Glass time series model Mathematics Subject Classification 34A07 • 35R13 Communicated by Anibal Tavares de Azevedo.

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Section: A Brief Review On the Differentiability Of Fuzzy-valued Funcmentioning

confidence: 99%

Fuzzy delay differential equations under granular differentiability with applications

Son¹,

Long

Dong

2019

Comp. Appl. Math.

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“…Differently of a fuzzy initial value problem where the derivative is obtained by a fuzzy process [2,4], here we only used numerical methods for FIVPs provided in the literature, to observe how the relationship of interactivity acts in the chemical reagents when the initial conditions were given by interactive fuzzy numbers.…”

Section: Final Remarksmentioning

confidence: 99%

Numerical Solution for Lotka-Volterra Model of Oscillating Chemical Reactions with Interactive Fuzzy Initial Conditions

Wasques

Esmi

Barros

et al. 2019

Proceedings of the 2019 Conference of the International Fuzzy Systems Association and the European Society for Fuzzy Logic and

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In this paper we study Lotka-Volterra model of oscillating chemical reactions via fuzzy differential equations, where the initial conditions are given by interactive fuzzy numbers. The concept of interactivity is associated with the notion of joint possibility distribution. The fuzzy solution is given by a numerical method which considers fuzzy arithmetic with interactivity. We present some examples to illustrate that different types of interactivity produce different solutions.

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“…ese kinds of problems might be difficult to solve directly and obtaining exact solutions is not always possible. erefore, researchers were interested in obtaining numerical solutions by using different methods, such as the decomposition method [15], the homotopy analysis method [14,16], the Runge-Kutta method [17,18], the least-square method [19], the interactive and standard arithmetic [20][21][22], the Fréchet derivative method [23], and solving delay fuzzy problems [24]. For more references, see [25,26,[33][34][35][36].…”

Section: Introductionmentioning

confidence: 99%

Optimization of One‐Step Block Method for Solving Second‐Order Fuzzy Initial Value Problems

Al-Refai¹,

Syam²,

Al-Refai

2021

Complexity

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Fréchet derivative for linearly correlated fuzzy function

Cited by 61 publications

References 13 publications

Fuzzy delay differential equations under granular differentiability with applications

Fuzzy delay differential equations under granular differentiability with applications

Numerical Solution for Lotka-Volterra Model of Oscillating Chemical Reactions with Interactive Fuzzy Initial Conditions

Optimization of One‐Step Block Method for Solving Second‐Order Fuzzy Initial Value Problems

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