Numerically solution of fuzzy differential equations by Adomian method

In this paper, we use the modified reproducing kernel Hilbert space method to approximate the solution of fuzzy differential equations of fractional order. Using this method, we construct a new algorithm to approximate the solution of such differential equations. The proposed algorithm produces solutions in terms of interval-valued fuzzy numbers. Two numerical examples are tested and the results showed that the proposed algorithm is able to produce solutions that approach to the exact solutions. It concludes that the proposed algorithm can be considered as a modern algorithm that complements to the existing ones. c ○2017 All rights reserved.Keywords: Caputo fractional derivative, fuzzy differential equation of fractional order, modified reproducing kernel Hilbert space method. 2010 MSC: 34A08, 34A07, 47B32.

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“…For more details on r-cut of fuzzy numbers, please see in [13,15,16,25,39]. Fuzzy numbers are often classified into membership function.…”

Section: Definition 22 ([32]mentioning

confidence: 99%

Approximate solutions of fuzzy differential equations of fractional order using modified reproducing kernel Hilbert space method

Albzeirat¹,

Ahmad²,

Momani³

et al. 2017

J. Nonlinear Sci. Appl.

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“…In section 3 we define the problem, this is a fuzzy Cauchy problem [11,9] whose numerical solution is the main interest of this work and we apply the standard Euler method for systems [1,7,8,13] followed by a complete error analysis and show that the numerical solution converges to the unique solution.…”

Section: The Journal Of Mathematics and Computer Sciencementioning

confidence: 99%

Comparison Of Two Methods For Solving Fuzzy Differential Equations Based On Euler Method And Zadeh's Extension

Najafi¹,

Sasemasi²,

Roudkoli³

et al. 2011

J. Math. Computer Sci.

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“…For a numerical approach, see [4,5,20,27]. Fuzzy functional differential equations with delay and some impulsive fuzzy differential equations have been studied in [25,36].…”

Section: Preliminariesmentioning

confidence: 99%

Monotone method for fuzzy differential equations

Rodríguez‐López

2008

Fuzzy Sets and Systems

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Numerically solution of fuzzy differential equations by Adomian method

Cited by 35 publications

References 12 publications

Approximate solutions of fuzzy differential equations of fractional order using modified reproducing kernel Hilbert space method

Approximate solutions of fuzzy differential equations of fractional order using modified reproducing kernel Hilbert space method

Comparison Of Two Methods For Solving Fuzzy Differential Equations Based On Euler Method And Zadeh's Extension

Monotone method for fuzzy differential equations

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