Fuzzy Sumudu transform for solving fuzzy partial differential equations

Rahman, Norazrizal Aswad Abdul; Ahmad, Muhammad Zaini

doi:10.22436/jnsa.009.05.111

Cited by 20 publications

(10 citation statements)

References 22 publications

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“…Using this property, researcher might have an insight or idea on the behaviour of the solutions as the variable approaches certain values or numbers. In other words, the transformed function can be treated as the replica of the original function rather than as dummies which happen when considering different type of fuzzy integral transform such as fuzzy Laplace transform [13]. Furthermore, FST have been applied to several types of fuzzy differential equations, for example, fuzzy differential equations with fractional order derivatives in [14] and [15], and fuzzy partial derivatives [13] as well as fuzzy integral equations [16].…”

Section: Introductionmentioning

confidence: 99%

Fuzzy Sumudu Decomposition Method for Fuzzy Delay Differential Equations with Strongly Generalized Differentiability

Rahman¹

2020

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Fuzzy delay differential equation has always been a tremendous way to model real-life problems. It has been developed throughout the last decade. Many types of fuzzy derivatives have been considered, including the recently introduced concept of strongly generalized differentiability. However, considering this interpretation, very few methods have been introduced, obstructing the potential of fuzzy delay differential equations to be developed further. This paper aims to provide solution for fuzzy nonlinear delay differential equations and the derivatives considered in this paper is interpreted using the concept of strongly generalized differentiability. Under this method, the calculations will lead to two cases i.e. two solutions, and one of the solutions is decreasing in the diameter. To fulfil this, a method resulting from the elegant combination of fuzzy Sumudu transform and Adomian decomposition method is used, it is termed as fuzzy Sumudu decomposition method. A detailed procedure for solving fuzzy nonlinear delay differential equations with the mentioned type of derivatives is constructed in detail. A numerical example is provided afterwards to demonstrate the applicability of the method. It is shown that the solution is not unique, and this is in accord with the concept of strongly generalized differentiability. The two solutions can later be chosen by researcher with regards to the characteristic of the problems. Finally, conclusion is drawn.

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Section: Introductionmentioning

confidence: 99%

Fuzzy Sumudu Decomposition Method for Fuzzy Delay Differential Equations with Strongly Generalized Differentiability

Rahman¹

2020

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“…In [24], Sumudu transform is applied to the system of differential equations. In [1], Sumudu transform is used in order to find the solution of fuzzy partial differential equations. In [23], Sumudu transform has been used to solve fractional differential equations.…”

Section: Introductionmentioning

confidence: 99%

Solving Differential Equations with Z-Numbers by Utilizing Fuzzy Sumudu Transform

Jafari

Razvarz

Gegov

2018

Advances in Intelligent Systems and Computing

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The uncertain nonlinear systems can be modeled with fuzzy differential equations (FDEs) and the solutions of these equations are applied to analyze many engineering problems. However, it is very difficult to obtain solutions of FDEs. In this paper, the solutions of FDEs are approximated by utilizing the fuzzy Sumudu transform (FST) method. Here, the uncertainties are in the sense of Z-numbers. Important theorems are laid down to illustrate the properties of FST. The theoretical analysis and simulation results show that this new technique is effective to estimate the solutions of FDEs.

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“…In [20], Sumudu transform is applied to the system of differential equations. In [21], Sumudu transform is used in order to find the solution of the fuzzy partial differential equation. In [22], Sumudu transform has been used to solve fractional differential equations.…”

Section: Introductionmentioning

confidence: 99%

Numerical Solution of Fuzzy Differential Equations with Z-numbers using Fuzzy Sumudu Transforms

Razvarz

Jafari

2018

Adv. sci. technol. eng. syst. j.

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Fuzzy Sumudu transform for solving fuzzy partial differential equations

Cited by 20 publications

References 22 publications

Fuzzy Sumudu Decomposition Method for Fuzzy Delay Differential Equations with Strongly Generalized Differentiability

Fuzzy Sumudu Decomposition Method for Fuzzy Delay Differential Equations with Strongly Generalized Differentiability

Solving Differential Equations with Z-Numbers by Utilizing Fuzzy Sumudu Transform

Numerical Solution of Fuzzy Differential Equations with Z-numbers using Fuzzy Sumudu Transforms

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