Numerical solution of fuzzy differential equations under generalized differentiability

Nieto, Juan J.; Khastan, A.; Ivaz, Karim

doi:10.1016/j.nahs.2009.06.013

Cited by 90 publications

(51 citation statements)

References 21 publications

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“…This example is a special case of FFDE which we solve it with our method and show that the numerical results of the two methods are the same. It is notable that all the results obtained in the our numerical method is similar to the results of Nieto et al in [28]. Therefore, solving this examples shows that our numerical method is capable of solving FDE and FFDE.…”

Section: Examplessupporting

confidence: 86%

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Fifth order Runge-Kutta method for solving first-order fully fuzzy differential equations under strongly generalized H-differentiability

Vivek¹,

Kanagarajan²

2016

Journal of Nonlinear Analysis and Application

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In this paper we use fifth order Runge-Kutta method for solving fully fuzzy differential equations of the form yThe algorithm used here are based on cross product of two fuzzy numbers. Using cross product we can divide fully fuzzy differential equation (FFDE) into four different cases. We apply the results to a particular case of FFDE. The Convergence of this method is discussed and numerical examples are given to verify the reliability of this method.

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Section: Examplessupporting

confidence: 86%

“…Therefore, on I 1 In the next example, a numerical method to solve the first-order fuzzy differential equations (FDE) (i.e., coefficient is crisp) is proposed in [28]. This example is a special case of FFDE which we solve it with our method and show that the numerical results of the two methods are the same.…”

Section: Examplesmentioning

confidence: 90%

Fifth order Runge-Kutta method for solving first-order fully fuzzy differential equations under strongly generalized H-differentiability

Vivek¹,

Kanagarajan²

2016

Journal of Nonlinear Analysis and Application

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“…A fuzzy set u in X is characterized by its membership function u : X → [0, 1]. Then, u(x) is interpreted as the degree of membership of an element x in the fuzzy set u for each x ∈ X [16].…”

Section: Preliminariesmentioning

confidence: 99%

“…Let L > 0 be the constant defined in the Lipschitz condition (16). Define γ := Lβ where β > 1 is an arbitrary constant.…”

mentioning

confidence: 99%

On Existence and Uniqueness of Solutions to the Fuzzy Dynamic Equations on Time Scales

Fard

Bidgoli

Rivaz

2017

MCA

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Abstract:In this paper, we introduce a new metric on the space of fuzzy continuous functions on time scales by using the exponential function, e γ (t, t 0 ), where γ > 0 is a constant. Then, we provide some conditions to prove an existence and uniqueness theorem for solutions to nonlinear fuzzy dynamic equations. Furthermore, we present three different examples including a practical example to illustrate the main results.

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“…The generalized Euler method based on the first-order approximation of [23] and represented as follow:…”

Section: Theorem 2 Letmentioning

confidence: 99%

Optimal Control Of Hiv Infection By Using Fuzzy Dynamical Systems

Najariyan¹,

Farahi²,

Alavian³

2011

J. Math. Computer Sci.

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A dynamical system represent the infection and propagation of HIV is considered. First a mathematical model for the HIV is simulated. Since age, sex… are important parameters in treatment of HIV disease, it is natural to consider the variables as fuzzy variables. Thus we need to consider a fuzzy dynamical system to control the HIV disease. To solve such a fuzzy dynamical system, by using α-cuts, one can convert this system to a non-fuzzy system of differential equations, then by using numerical methods one may attempts to solve these differential equations

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Numerical solution of fuzzy differential equations under generalized differentiability

Cited by 90 publications

References 21 publications

Fifth order Runge-Kutta method for solving first-order fully fuzzy differential equations under strongly generalized H-differentiability

Fifth order Runge-Kutta method for solving first-order fully fuzzy differential equations under strongly generalized H-differentiability

On Existence and Uniqueness of Solutions to the Fuzzy Dynamic Equations on Time Scales

Optimal Control Of Hiv Infection By Using Fuzzy Dynamical Systems

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