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New Configurations of the Fuzzy Fractional Differential Boussinesq Model with Application in Ocean Engineering and Their Analysis in Statistical Theory
Yu-Ming Chu1, Saima Rashid2,*, Shazia Karim3, Anam Sultan2
1
Department of Mathematics, Huzhou University, Huzhou, 313000, China
2
Department of Mathematics, Government College University, Faisalabad, 38000, Pakistan
3
Department of Basic Sciences and Humanities, UET Lahore, Faisalabad Campus, Lahore, Pakistan
* Corresponding Author: Saima Rashid. Email:
Computer Modeling in Engineering & Sciences 2023, 137(2), 1573-1611. https://doi.org/10.32604/cmes.2023.027724
Received 11 November 2022; Accepted 21 February 2023; Issue published 26 June 2023
Abstract
The fractional-order Boussinesq equations (FBSQe) are investigated in this work to see if they can effectively
improve the situation where the shallow water equation cannot directly handle the dispersion wave. The fuzzy
forms of analytical FBSQe solutions are first derived using the Adomian decomposition method. It also occurs on
the sea floor as opposed to at the functionality. A set of dynamical partial differential equations (PDEs) in this
article exemplify an unconfined aquifer flow implication. This methodology can accurately simulate climatological
intrinsic waves, so the ripples are spread across a large demographic zone. The Aboodh transform merged with the
mechanism of Adomian decomposition is implemented to obtain the fuzzified FBSQe in

and (2nth)-order
involving generalized Hukuhara differentiability. According to the system parameter, we classify the qualitative
features of the Aboodh transform in the fuzzified Caputo and Atangana-Baleanu-Caputo fractional derivative
formulations, which are addressed in detail. The illustrations depict a comparison analysis between the both
fractional operators under gH-differentiability, as well as the appropriate attributes for the fractional-order and
unpredictability factors σ ∈ [0, 1]. A statistical experiment is conducted between the findings of both fractional
derivatives to prevent changing the hypothesis after the results are known. Based on the suggested analyses,
hydrodynamic technicians, as irrigation or aquifer quality experts, may be capable of obtaining an appropriate
storage intensity amount, including an unpredictability threshold.
Keywords
Fuzzy set theory; aboodh transform; adomian decomposition method; boussinesq equation; fractional derivative operators; analysis of variance test
Cite This Article
APA Style
Chu, Y., Rashid, S., Karim, S., Sultan, A. (2023). New Configurations of the Fuzzy Fractional Differential Boussinesq Model with Application in Ocean Engineering and Their Analysis in Statistical Theory.
Computer Modeling in Engineering & Sciences,
137(2), 1573–1611.
https://doi.org/10.32604/cmes.2023.027724
Vancouver Style
Chu Y, Rashid S, Karim S, Sultan A. New Configurations of the Fuzzy Fractional Differential Boussinesq Model with Application in Ocean Engineering and Their Analysis in Statistical Theory. Comput Model Eng Sci. 2023;137(2):1573–1611.
https://doi.org/10.32604/cmes.2023.027724
IEEE Style
Y. Chu, S. Rashid, S. Karim, and A. Sultan, “New Configurations of the Fuzzy Fractional Differential Boussinesq Model with Application in Ocean Engineering and Their Analysis in Statistical Theory,”
Comput. Model. Eng. Sci., vol. 137, no. 2, pp. 1573–1611, 2023.
https://doi.org/10.32604/cmes.2023.027724

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