Solving fuzzy fractional differential equations with applications

Osman, M. T. Abu; Xia, Yonghui

doi:10.1016/j.aej.2023.01.056

Cited by 3 publications

(3 citation statements)

References 55 publications

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“…Theorem 5.2 Let P n k¼0 W k ðI; B; }Þ shows the approximation of Eq (16), ultimately the absolute error is identified as…”

Section: Convergence Analysismentioning

confidence: 99%

“…Fuzzy integral equations have several applications in various practical problems such as industrial engineering, scientific computing, physical sciences and neural network. It is studied that the existing study problem with fractional order derivatives can be turned to uncertain problems [15,16]. As a result, several scholars focused on such frameworks in order to examine their solutions analytically or numerically.…”

Section: Introductionmentioning

confidence: 99%

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Analytical solution of fuzzy heat problem in two-dimensional case under Caputo-type fractional derivative

Nadeem,

Yilin,

Kumar

et al. 2024

PLoS ONE

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This work aims to investigate the analytical solution of a two-dimensional fuzzy fractional-ordered heat equation that includes an external diffusion source factor. We develop the Sawi homotopy perturbation transform scheme (SHPTS) by merging the Sawi transform and the homotopy perturbation scheme. The fractional derivatives are examined in Caputo sense. The novelty and innovation of this study originate from the fact that this technique has never been tested for two-dimensional fuzzy fractional ordered heat problems. We presented two distinguished examples to validate our scheme, and the solutions are in fuzzy form. We also exhibit contour and surface plots for the lower and upper bound solutions of two-dimensional fuzzy fractional-ordered heat problems. The results show that this approach works quite well for resolving fuzzy fractional situations.

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“…Theorem 5.2 Let P n k¼0 W k ðI; B; }Þ shows the approximation of Eq (16), ultimately the absolute error is identified as…”

Section: Convergence Analysismentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Analytical solution of fuzzy heat problem in two-dimensional case under Caputo-type fractional derivative

Nadeem,

Yilin,

Kumar

et al. 2024

PLoS ONE

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“…Many mathematicians are interested in fuzzy fractional differential equations (FFDEs) and fuzzy fractional calculus since these theories are helpful in determining uncertainty influenced by ambiguity and inaccuracy. The concepts of Riemann-Liouville, Caputo-Hadamard, Caputo-Katugampola, Caputo-Atangana-Baleanu, Caputo-Fabrizio derivatives, and Caputo fuzzy fractional integrals and/or derivative operators have been applied in the majority of articles presented to date on this topic (see [10][11][12][13][14][15][16][17][18][19][20][21][22]).…”

Section: Introductionmentioning

confidence: 99%

Local Fuzzy Fractional Partial Differential Equations in the Realm of Fractal Calculus with Local Fractional Derivatives

Osman,

Marwan,

Shah

et al. 2023

Fractal Fract

Self Cite

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In this study, local fuzzy fractional partial differential equations (LFFPDEs) are considered using a hybrid local fuzzy fractional approach. Fractal model behavior can be represented using fuzzy partial differential equations (PDEs) with local fractional derivatives. The current methods are hybrids of the local fuzzy fractional integral transform and the local fuzzy fractional homotopy perturbation method (LFFHPM), the local fuzzy fractional Sumudu decomposition method (LFFSDM) in the sense of local fuzzy fractional derivatives, and the local fuzzy fractional Sumudu variational iteration method (LFFSVIM); these are applied when solving LFFPDEs. The working procedure shows how effective solutions for specific LFFPDEs can be obtained using the applied approaches. Moreover, we present a comparison of the local fuzzy fractional Laplace variational iteration method (LFFLIM), the local fuzzy fractional series expansion method (LFFSEM), the local fuzzy fractional variation iteration method (LFFVIM), and the local fuzzy fractional Adomian decomposition method (LFFADM), which are applied to obtain fuzzy fractional diffusion and wave equations on Cantor sets. To demonstrate the effectiveness of the used techniques, some examples are given. The results demonstrate the major advantages of the approaches, which are equally efficient and simple to use in order to solve fuzzy differential equations with local fractional derivatives.

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A modified fuzzy Adomian decomposition method for solving time-fuzzy fractional partial differential equations with initial and boundary conditions

Saeed,

Pachpatte

2024

Bound Value Probl

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This research article introduces a novel approach based on the fuzzy Adomian decomposition method (FADM) to solve specific time fuzzy fractional partial differential equations with initial and boundary conditions (IBCs). The proposed approach addresses the challenge of incorporating both initial and boundary conditions into the FADM framework by employing a modified approach. This approach iteratively generates a new initial solution using the decomposition method. The method presented here offers a significant contribution to solving fuzzy fractional partial differential equations (FFPDEs) with fuzzy IBCs, a topic that has received limited attention in the literature. Furthermore, it satisfies a high convergence rate with minimal computational complexity, establishing a novel aspect of this research. By providing a series solution with a small number of recursive formulas, this method enhances accuracy and emerges as a preferred choice for tackling FFPDEs with mixed initial and boundary conditions. The effectiveness of the proposed technique is further supported by the inclusion of several illustrative examples.

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Solving fuzzy fractional differential equations with applications

Cited by 3 publications

References 55 publications

Analytical solution of fuzzy heat problem in two-dimensional case under Caputo-type fractional derivative

Analytical solution of fuzzy heat problem in two-dimensional case under Caputo-type fractional derivative

Local Fuzzy Fractional Partial Differential Equations in the Realm of Fractal Calculus with Local Fractional Derivatives

A modified fuzzy Adomian decomposition method for solving time-fuzzy fractional partial differential equations with initial and boundary conditions

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