On the solutions of first-order linear impulsive fuzzy differential equations

Liu, Rui; Wang, JinRong; O’Regan, Donal

doi:10.1016/j.fss.2019.11.001

Cited by 16 publications

(4 citation statements)

References 21 publications

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“…As a result, numerous scholars have focused on studying fuzzy fractional differential equations in diverse directions. In [12][13][14][15], several basic difficulties are investigated. The Atangana-Baleanu Caputo derivative [16], a nonsingular fractional derivative suggested by Attangana, Balaneau, and Caputo, has recently gained prominence among scholars [17][18][19][20].…”

Section: Introductionmentioning

confidence: 99%

Novel Analysis of Fuzzy Physical Models by Generalized Fractional Fuzzy Operators

Alaoui

Alharbi

Zaland

2022

Journal of Function Spaces

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The present article correlates with a fuzzy hybrid technique combined with an iterative transformation technique identified as the fuzzy new iterative transform method. With the help of Atangana-Baleanu under generalized Hukuhara differentiability, we demonstrate the consistency of this method by achieving fuzzy fractional gas dynamics equations with fuzzy initial conditions. The achieved series solution was determined and contacted the estimated value of the suggested equation. To confirm our technique, three problems have been presented, and the results were estimated in fuzzy type. The lower and upper portions of the fuzzy solution in all three examples were simulated using two distinct fractional orders between 0 and 1. Because the exponential function is present, the fractional operator is nonsingular and global. It provides all forms of fuzzy solutions occurring between 0 and 1 at any fractional-order because it globalizes the dynamical behavior of the given equation. Because the fuzzy number provides the solution in fuzzy form, with upper and lower branches, fuzziness is also incorporated in the unknown quantity. It is essential to mention that the projected methodology to fuzziness is to confirm the superiority and efficiency of constructing numerical results to nonlinear fuzzy fractional partial differential equations arising in physical and complex structures.

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Section: Introductionmentioning

confidence: 99%

Novel Analysis of Fuzzy Physical Models by Generalized Fractional Fuzzy Operators

Alaoui

Alharbi

Zaland

2022

Journal of Function Spaces

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show abstract

“…As a result, numerous scholars have focused on analyzing fractional fuzzy differential models in diverse directions. In [7][8][9], several fundamental difficulties are investigated. The Atangana-Baleanu-Caputo derivative [10], a fractional nonsingular derivative proposed by Atangana, Baleanu, and Caputo, has recently gained prominence among scholars [11,12].…”

Section: Introductionmentioning

confidence: 99%

Study of Fuzzy Fractional Nonlinear Equal Width Equation in the Sense of Novel Operator

Naeem

Khammash

Mahariq

et al. 2021

Journal of Function Spaces

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In this paper, we designed an algorithm by applying the Laplace transform to calculate some approximate solutions for fuzzy fractional-order nonlinear equal width equations in the sense of Atangana-Baleanu-Caputo derivatives. By analyzing the fuzzy theory, the suggested technique helps the solution of the fuzzy nonlinear equal width equations be investigated as a series of expressions in which the components can be effectively recognised and produce a pair of numerical results with the uncertainty parameters. Several numerical examples are analyzed to validate convergence outcomes for the given problem to show the proposed method’s utility and capability. The simulation outcomes reveal that the fuzzy iterative transform method is an effective method for accurately and precisely studying the behavior of suggested problems. We test the developed algorithm by three different problems. The analytical analysis provided that the results of the models converge to their actual solutions at the integer-order. Furthermore, we find that the fractional derivative produces a wide range of fuzzy results.

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“…Therefore, many researchers have been worked on the area of fuzzy fractional differential equations (FFDEs) to investigate them in various direction. Some elementary problems are investigated in [24][25][26].…”

Section: Introductionmentioning

confidence: 99%

Study of fuzzy fractional order diffusion problem under the Mittag-Leffler Kernel Law

Arfan¹,

Shah²,

Ullah³

et al. 2021

Phys. Scr.

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Our research work is composed of designing the scheme for computation of some analytical results for fractional order fuzzy diffusion problem under Atangana-Baleanu and Caputo (    ) fractional differential operator. We have obtained the required series type solution by using the Laplace transform along with decomposition techniques. By applying the said method, we have decomposed the required whole quantity into small parts and calculate the series solution for the first few terms We have tested the develop algorithm by three different problems of one, two and three dimensions. The numerical simulations confirm that the solutions of the problems converge to their exact values at the integer-order. Further, we conclude that the fractional-order derivative yields a complete spectrum of fuzzy solutions.

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On the solutions of first-order linear impulsive fuzzy differential equations

Cited by 16 publications

References 21 publications

Novel Analysis of Fuzzy Physical Models by Generalized Fractional Fuzzy Operators

Novel Analysis of Fuzzy Physical Models by Generalized Fractional Fuzzy Operators

Study of Fuzzy Fractional Nonlinear Equal Width Equation in the Sense of Novel Operator

Study of fuzzy fractional order diffusion problem under the Mittag-Leffler Kernel Law

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