An efficient analytical-numerical technique for handling model of fuzzy differential equations of fractional-order

Alaroud, Mohammad; Rozita, Rokiah Ahmad; Khair, Ummul Din

doi:10.2298/fil1902617a

Cited by 15 publications

(4 citation statements)

References 25 publications

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“…For α � 1, the series expansions (46) have the form, y 1 (t) � e t sin t and y 2 (t) � e t cos t which are coincide with the exact solutions for the ordinary system ( 27) and (28).…”

Section: Numerical Examplesmentioning

confidence: 67%

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Application of ARA-Residual Power Series Method in Solving Systems of Fractional Differential Equations

Qazza

Burqan

Saadeh

2022

Mathematical Problems in Engineering

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In this research, systems of linear and nonlinear differential equations of fractional order are solved analytically using the novel interesting method: ARA- Residual Power Series (ARA-RPS) technique. This approach technique is based on the combination of the residual power series scheme with the ARA transform to establish analytical approximate solutions in a fast convergent series representation using the concept of the limit. The proposed method needs less time and effort compared with the residual power series technique. To prove the simplicity, applicability, and reliability of the presented method, three numerical examples are proposed and simulated. The obtained results show that the ARA-RPS technique is applicable, simple, and effective to get solutions to linear and nonlinear engineering and physical problems.

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“…For α � 1, the series expansions (46) have the form, y 1 (t) � e t sin t and y 2 (t) � e t cos t which are coincide with the exact solutions for the ordinary system ( 27) and (28).…”

Section: Numerical Examplesmentioning

confidence: 67%

“…In this paper, we employ the ARA-RPS method to investigate analytical and approximate solutions of linear and nonlinear systems of FDEs. e ARA-RPS technique that has been introduced in [39] is a combination of the ARA transform [37][38][39] and the residual power series method [40][41][42][43][44][45][46][47].…”

Section: Introductionmentioning

confidence: 99%

Application of ARA-Residual Power Series Method in Solving Systems of Fractional Differential Equations

Qazza

Burqan

Saadeh

2022

Mathematical Problems in Engineering

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“…However, several mathematical techniques have been employed to investigate their solutions. For example, homotopy analysis technique, variational iteration technique, Adomian decomposition technique, residual power series technique, and other techniques are some of these methods, and for more details, see [21,[26][27][28][29][30][31][32][33].…”

Section: Introductionmentioning

confidence: 99%

An Attractive Approach Associated with Transform Functions for Solving Certain Fractional Swift-Hohenberg Equation

Alaroud

Tahat

Al‐Omari

et al. 2021

Journal of Function Spaces

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Many phenomena in physics and engineering can be built by linear and nonlinear fractional partial differential equations which are considered an accurate instrument to interpret these phenomena. In the current manuscript, the approximate analytical solutions for linear and nonlinear time-fractional Swift-Hohenberg equations are created and studied by means of a recent superb technique, named the Laplace residual power series (LRPS) technique under the time-Caputo fractional derivatives. The proposed technique is a combination of the generalized Taylor’s formula and the Laplace transform operator, which depends mainly on the concept of limit at infinity to find the unknown functions for the fractional series expansions in the Laplace space with fewer computations and more accuracy comparing with the classical RPS that depends on the Caputo fractional derivative for each step in obtaining the coefficient expansion. To test the simplicity, performance, and applicability of the present method, three numerical problems of the time-fractional Swift-Hohenberg initial value problems are considered. The impact of the fractional order β on the behavior of the approximate solutions at fixed bifurcation parameter is shown graphically and numerically. Obtained results emphasized that the LRPS technique is an easy, efficient, and speed approach for the exact description of the linear and nonlinear time-fractional models that arise in natural sciences.

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“…This technique needs less computational requirements with high precision as well as less time. Recently, very few researchers have studied the solution of fuzzy DE using the RPSM [18–21].…”

Section: Introductionmentioning

confidence: 99%

Analysis of time‐fractional fuzzy vibration equation of large membranes using double parametric based Residual power series method

Jena

Sedighi

2020

Z Angew Math Mech

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The study of the time‐fractional vibration equation (VE) of large membranes is vital due to its widespread applications. Various researchers have investigated the titled problem in which the variables and parameters have been considered as crisp/exact. However, in actual practice, this may contain uncertainty because of errors in observations, maintenance induced error, and other errors. In this investigation, we have considered these uncertainties as interval/fuzzy, and a method, namely double parametric form of fuzzy numbers are used to solve the uncertain fractional vibration model of order α(1<α≤2). The titled problem has been solved under various cases using the Residual power series method (RPSM). The performance of the present method is well in terms of computational efficiency. The consistency of the method is displayed by providing numerical solutions for various cases. Obtained results are depicted in terms of figures and are also compared with individual cases.

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An efficient analytical-numerical technique for handling model of fuzzy differential equations of fractional-order

Cited by 15 publications

References 25 publications

Application of ARA-Residual Power Series Method in Solving Systems of Fractional Differential Equations

Application of ARA-Residual Power Series Method in Solving Systems of Fractional Differential Equations

An Attractive Approach Associated with Transform Functions for Solving Certain Fractional Swift-Hohenberg Equation

Analysis of time‐fractional fuzzy vibration equation of large membranes using double parametric based Residual power series method

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