Solving fuzzy fractional differential equations using fuzzy Sumudu transform

Rahman, Norazrizal Aswad Abdul; Ahmad, Muhammad Zaini

doi:10.22436/jnsa.010.05.28

Cited by 20 publications

(6 citation statements)

References 30 publications

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“…In this section, assume that the FIC is [T h (0)] -= [T(0)] -= [1,2,3]. Taking % = & = 1 for Cases i and j so, % = −1, & = 1 for Cases ii and jj.…”

Section: Main Results and Discussionmentioning

confidence: 99%

“…In [37], this new transform was applied to find analytical solutions of fractional-order heat and wave equations. In the recent years and with the rapid development of linear and nonlinear science, many effectiveness numerical and analytical different methods for solving the fuzzy fractional differential equations, as using the fuzzy Laplace and fuzzy Sumudu transforms, see ( [1], [14]). The objective of this paper is to discuss the numerically solutions for each form and system of FFODEs based on orders of fuzzy Caputo's H-difference by using FNT.…”

Section: Introductionmentioning

confidence: 99%

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Solution of Linear Fuzzy Fractional Differential Equations Using Fuzzy Natural Transform

Al-Humedi

Kadhim

2021

EJMS

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The purpose of this paper is to apply the fuzzy natural transform (FNT) for solving linear fuzzy fractional ordinary differential equations (FFODEs) involving fuzzy Caputo’s H-difference with Mittag-Leffler laws. It is followed by proposing new results on the property of FNT for fuzzy Caputo’s H-difference. An algorithm was then applied to find the solutions of linear FFODEs as fuzzy real functions. More specifically, we first obtained four forms of solutions when the FFODEs is of order α∈(0,1], then eight systems of solutions when the FFODEs is of order α∈(1,2] and finally, all of these solutions are plotted using MATLAB. In fact, the proposed approach is an effective and practical to solve a wide range of fractional models.

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“…In this section, assume that the FIC is [T h (0)] -= [T(0)] -= [1,2,3]. Taking % = & = 1 for Cases i and j so, % = −1, & = 1 for Cases ii and jj.…”

Section: Main Results and Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Solution of Linear Fuzzy Fractional Differential Equations Using Fuzzy Natural Transform

Al-Humedi

Kadhim

2021

EJMS

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“…The applications of the said calculus in physics may be studied in [3]. Some fuzzy fractional-order linear and non-linear dynamical problems have been analyzed for semi-analytical solutions using fractional Sumudo transform [4,5]. Many types of publications have also been based on existence, uniqueness and numerical analysis under fractional-order concepts.…”

Section: Introductionmentioning

confidence: 99%

“…Among them are the well-known integral transforms of Fourier, Natural, Z, Laplace, Sumudu, etc. [4,15,16]. Some of the iterative and series solution methods such as the "homotopy and improved homotopy method" [17][18][19], Adomian decomposition along with Adomian polynomial and Laplace Adomian decomposition methods (LADM) [20,21], "Taylor's" series method, etc.…”

Section: Introductionmentioning

confidence: 99%

Semi-Analytical Solutions for Fuzzy Caputo–Fabrizio Fractional-Order Two-Dimensional Heat Equation

et al. 2021

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In the analysis in this article, we developed a scheme for the computation of a semi-analytical solution to a fuzzy fractional-order heat equation of two dimensions having some external diffusion source term. For this, we applied the Laplace transform along with decomposition techniques and the Adomian polynomial under the Caputo–Fabrizio fractional differential operator. Furthermore, for obtaining a semi-analytical series-type solution, the decomposition of the unknown quantity and its addition established the said solution. The obtained series solution was calculated and approached the approximate solution of the proposed equation. For the validation of our scheme, three different examples have been provided, and the solutions were calculated in fuzzy form. All the three illustrations simulated two different fractional orders between 0 and 1 for the upper and lower portions of the fuzzy solution. The said fractional operator is nonsingular and global due to the presence of the exponential function. It globalizes the dynamical behavior of the said equation, which is guaranteed for all types of fuzzy solution lying between 0 and 1 at any fractional order. The fuzziness is also included in the unknown quantity due to the fuzzy number providing the solution in fuzzy form, having upper and lower branches.

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“…were suggested in the past. Laplace transforms [33,11,7,1,52,58] are widely used to solve the differential and integral equations. Later on, the Sumudu transform was introduced in 1993 and then extended to two variables by the same author in 2002 [10].…”

mentioning

confidence: 99%

A novel semi-analytical method for solutions of two dimensional fuzzy fractional wave equation using natural transform

Arfan¹,

Shah²,

Ullah³

et al. 2022

DCDS-S

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In this research article, the techniques for computing an analytical solution of 2D fuzzy wave equation with some affecting term of force has been provided. Such type of achievement for the aforesaid solution is obtained by applying the notions of a Caputo non-integer derivative in the vague or uncertainty form. At the first attempt the fuzzy natural transform is applied for obtaining the series solution. Secondly the homotopy perturbation (HPM) technique is used, for the analysis of the proposed result by comparing the co-efficient of homotopy parameter q to get hierarchy of equation of different order for q . For this purpose, some new results about Natural transform of an arbitrary derivative under uncertainty are established, for the first time in the literature. The solution has been assumed in term of infinite series, which break the problem to a small number of equations, for the respective investigation. The required results are then determined in a series solution form which goes rapidly towards the analytical result. The solution has two parts or branches in fuzzy form, one is lower branch and the other is upper branch. To illustrate the ability of the considered approach, we have proved some test problems.

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Solving fuzzy fractional differential equations using fuzzy Sumudu transform

Cited by 20 publications

References 30 publications

Solution of Linear Fuzzy Fractional Differential Equations Using Fuzzy Natural Transform

Solution of Linear Fuzzy Fractional Differential Equations Using Fuzzy Natural Transform

Semi-Analytical Solutions for Fuzzy Caputo–Fabrizio Fractional-Order Two-Dimensional Heat Equation

A novel semi-analytical method for solutions of two dimensional fuzzy fractional wave equation using natural transform

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