Stability of Fuzzy Differential Equations With the Second Type of Hukuhara Derivative

Zhang, Shuorui

doi:10.1109/tfuzz.2014.2353134

Cited by 9 publications

(4 citation statements)

References 27 publications

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“…As a result, the implicit method has the best stability properties. (2) Under the condition that the value of the normal fuzzy variable ξ is in the neighborhood of (1 − r)/s, if we increase α, i.e., going towards implicitness, the stability is improving but the fully implicit scheme is unstable again. This reveals that the implicit scheme is not a special case of the semi-implicit one, because the latter one handles the last term fully explicit.…”

Section: Remarkmentioning

confidence: 99%

“…The FDE studied by experts is the fuzzification of the classical differential equation. The essence is generally divided into three cases: (1) converting the coefficients into fuzzy numbers; (2) replacing the initial or boundary values with fuzzy numbers; and (3) the forcing term is a fuzzy-valued function. Therefore, the form of FDE is either one of three cases or a combination thereof.…”

Section: Introductionmentioning

confidence: 99%

“…The involving differential is defined according to different fuzzy derivatives, as the representative is the generalized differential and the generalized Hukuhara derivative. On the premise of the Hukuhara derivative, by using linear transformations, Ngo [1] obtained the expression for the exact solution of linear second-order FDE; Zhang and Sun [2] put forward some definitions of the stability of FDE under second-order Hukuhara derivatives by means of Lyapunov function. Related to solving FDE, Khastan et al [3,4] obtained new fuzzy approximation methods by fuzzy transform; Allahviranloo et al [5] raised an Euler scheme on the basis of Taylor expansion; and spline collocation methods for systems of fuzzy fractional differential equations were deduced by Alijani et al [6].…”

Section: Introductionmentioning

confidence: 99%

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Stability of Euler Methods for Fuzzy Differential Equation

You

Cheng

2022

Symmetry

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The Liu process is a fuzzy process whose membership function is a symmetric function on an expected value. The object of this paper was a fuzzy differential equation driven by Liu process. Since the existing fuzzy Euler solving methods (explicit Euler scheme, semi-implicit Euler scheme, and implicit Euler scheme) have the same convergence, to compare them, we presented four stabilities, i.e., asymptotical stability, mean square stability, exponential stability, and A stability. By choosing special fuzzy differential equation as a test equation, we deduced that mean square stability is equivalent to exponential stability. Furthermore, an explicit fuzzy Euler scheme and semi-implicit fuzzy Euler scheme showed asymptotical stability and mean square stability, while an explicit fuzzy Euler scheme failed to meet A stability but that an implicit fuzzy Euler scheme is A stable, and whether semi-implicit fuzzy Euler scheme is A stable depends on the values of α and λ.

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Section: Remarkmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Stability of Euler Methods for Fuzzy Differential Equation

You

Cheng

2022

Symmetry

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“…Further, Malinowski [24,25] studied the concept of second type Hukuhara derivative for interval differential equations and interval Cauchy problem with second type Hukuhara derivative. Furthermore, Zhang and Sun [36] studied the stability of FDEs under second type Hukuhara derivative.…”

Section: Introductionmentioning

confidence: 99%

Existence-uniqueness of solutions for fuzzy nabla initial value problems on time scales

et al. 2019

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This paper is devoted to studying the existence and uniqueness of solutions of fuzzy nabla dynamic equations on time scales under Hukuhara differentiability. We apply the Banach contraction mapping principle to establish existence and uniqueness solution for fuzzy nabla initial value problems on time scales and also obtain existence result using Ascoli's theorem and Schauder's fixed point theorem.

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Lyapunov stability of fuzzy dynamical systems based on fuzzy-number-valued function granular differentiability

Yang,

Chen

2024

Communications in Nonlinear Science and Numerical Simulation

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Stability of Fuzzy Differential Equations With the Second Type of Hukuhara Derivative

Cited by 9 publications

References 27 publications

Stability of Euler Methods for Fuzzy Differential Equation

Stability of Euler Methods for Fuzzy Differential Equation

Existence-uniqueness of solutions for fuzzy nabla initial value problems on time scales

Lyapunov stability of fuzzy dynamical systems based on fuzzy-number-valued function granular differentiability

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