Fuzzy Arbitrary Order System

Chakraverty, Snehashish; Tapaswini, Smita; Behera, Diptiranjan

doi:10.1002/9781119004233

Cited by 57 publications

(12 citation statements)

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“…However, in terms of Hukuhara differentiability, this notion was unable to achieve the large and diversified behavior of the crisp solution at the time. However, Bede and Stefanini and Allahviranloo et al [11,12] developed the Riemann-Liouville H-derivative in 2012, which was based on highly extended Hukuhara differ-entiability [13,14]. They also defined the fractional derivative of Riemann-Liouville.…”

Section: Introductionmentioning

confidence: 99%

Existence and Uniqueness of Mild Solution for Fractional-Order Controlled Fuzzy Evolution Equation

Iqbal

Niazi

Shafqat

et al. 2021

Journal of Function Spaces

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In this article, we investigated the existence and uniqueness of mild solutions for fractional-order controlled fuzzy evolution equations with Caputo derivatives of the controlled fuzzy nonlinear evolution equation of the form 0 c D I γ x I = α x I + P I , x I + A I W I , I ∈ 0 , T , x I 0 = x 0 , in which γ ∈ 0 , 1 , E 1 is the fuzzy metric space and I = 0 , T is a real line interval. With the help of few conditions on functions P : I × E 1 × E 1 ⟶ E 1 , W I is control and it belongs to E 1 , A ∈ F I , L E 1 , and α stands for the highly continuous fuzzy differential equation generator. Finally, a few instances of fuzzy fractional differential equations are shown.

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Section: Introductionmentioning

confidence: 99%

Existence and Uniqueness of Mild Solution for Fractional-Order Controlled Fuzzy Evolution Equation

Iqbal

Niazi

Shafqat

et al. 2021

Journal of Function Spaces

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“…Some researchers have found results about fuzzy differential equations in the literature, but most of them were for first-order differential equations or fractional orders between (0, 1]. In our work we have found results for Caputo derivatives of order (1,2); see [5,10,25] for more details. Our results are more complicated than the previous ones, and we require more boundary conditions than previous methods.…”

Section: Introductionmentioning

confidence: 53%

“…Until 2010, the concept in terms of Hukuhara differentiability [4] was unable to produce the vast and varied behavior of the crisp solution. However, later in 2012, a Riemann-Liouville H-derivative based on strongly generalized Hukuhara differentiability [5,6] was defined by Allahviranloo and Salahshour [7,8]. They also defined a fuzzy Riemann-Liouville fractional derivative.…”

Section: Introductionmentioning

confidence: 99%

Controllability for Fuzzy Fractional Evolution Equations in Credibility Space

et al. 2021

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This article addresses exact controllability for Caputo fuzzy fractional evolution equations in the credibility space from the perspective of the Liu process. The class or problems considered here are Caputo fuzzy differential equations with Caputo derivatives of order β∈(1,2), 0CDtβu(t,ζ)=Au(t,ζ)+f(t,u(t,ζ))dCt+Bx(t)Cx(t)dt with initial conditions u(0)=u0,u′(0)=u1, where u(t,ζ) takes values from U(⊂EN),V(⊂EN) is the other bounded space, and EN represents the set of all upper semi-continuously convex fuzzy numbers on R. In addition, several numerical solutions have been provided to verify the correctness and effectiveness of the main result. Finally, an example is given, which expresses the fuzzy fractional differential equations.

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“…Parameter concept is useful to convert an interval to crisp form. Accordingly, the interval x̃ = [ x̱, x̄ ] may be written as (Tapaswini and Chakraverty, 2014; Chakraverty et al , 2016a, 2016b) follows: where β ∈ [0,1] is a parameter and Δx˜=( xtrue¯ − xtrue¯ )2…”

Section: Preliminariesmentioning

confidence: 99%

“…Tapaswini and Chakraverty (2014) implemented Adomian decomposition method to solve uncertain beam equation by proposing a new technique based on double parametric form of fuzzy numbers. Further, Chakraverty et al (2016a, 2016b) extended the use of VIM and HPM for solving fuzzy ordinary, partial differential equations and fractional order differential equations.…”

Section: Introductionmentioning

confidence: 99%

Solving shallow water equations with crisp and uncertain initial conditions

Karunakar

Chakraverty

2018

HFF

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Purpose This paper aims to deal with the application of variational iteration method and homotopy perturbation method (HPM) for solving one dimensional shallow water equations with crisp and fuzzy uncertain initial conditions. Design/methodology/approach Firstly, the study solved shallow water equations using variational iteration method and HPM with constant basin depth and crisp initial conditions. Further, the study considered uncertain initial conditions in terms of fuzzy numbers, which leads the governing equations to fuzzy shallow water equations. Then using cut and parametric concepts the study converts fuzzy shallow water equations to crisp form. Then, HPM has been used to solve the fuzzy shallow water equations. Findings Results obtained by both methods HPM and variational iteration method are compared graphically in crisp case. Solution of fuzzy shallow water equations by HPM are presented in the form triangular fuzzy number plots. Originality/value Shallow water equations with crisp and fuzzy initial conditions have been solved.

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Fuzzy Arbitrary Order System

Cited by 57 publications

References 0 publications

Existence and Uniqueness of Mild Solution for Fractional-Order Controlled Fuzzy Evolution Equation

Existence and Uniqueness of Mild Solution for Fractional-Order Controlled Fuzzy Evolution Equation

Controllability for Fuzzy Fractional Evolution Equations in Credibility Space

Solving shallow water equations with crisp and uncertain initial conditions

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