Double Parametric Fuzzy Numbers Approximate Scheme for Solving One-Dimensional Fuzzy Heat-Like and Wave-Like Equations

Jameel, A. F.; Altaie, Sarmad A.; Aljabbari, Sardar Gul Amen; AlZubaidi, Abbas K.; Man, Noraziah Haji

doi:10.3390/math8101737

Cited by 5 publications

(2 citation statements)

References 25 publications

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“…Sakar et al [67] discussed the HPM applied to solve fractional PDEs with proportional delays. Jameel et al [68] presented the application of HPM to solving one-dimensional heat-like and wave-like equations in a fuzzy environment. Osman et al [40] investigated the comparison of fuzzy HPM and other methods to get the solutions of a fuzzy (1 + n)-dimensional Burgers' equation.…”

Section: Introductionmentioning

confidence: 99%

On the Fuzzy Solution of Linear-Nonlinear Partial Differential Equations

Osman

Xia²,

Omer³

et al. 2022

Mathematics

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In this article, we present the fuzzy Adomian decomposition method (ADM) and fuzzy modified Laplace decomposition method (MLDM) to obtain the solutions of fuzzy fractional Navier–Stokes equations in a tube under fuzzy fractional derivatives. We have looked at the turbulent flow of a viscous fluid in a tube, where the velocity field is a function of only one spatial coordinate, in addition to time being one of the dependent variables. Furthermore, we investigate the fuzzy Elzaki transform, and the fuzzy Elzaki decomposition method (EDM) applied to solving fuzzy linear-nonlinear Schrodinger differential equations. The proposed method worked perfectly without any need for linearization or discretization. Finally, we compared the fuzzy reduced differential transform method (RDTM) and fuzzy homotopy perturbation method (HPM) to solving fuzzy heat-like and wave-like equations with variable coefficients. The RDTM and HPM solutions are simpler than other already existing methods. Several examples are provided to illustrate the methods that have been offered. The results obtained using the scheme presented here agree well with the analytical solutions and the numerical results presented elsewhere. These studies are important in the context of the development of the theory of fuzzy partial differential equations.

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Section: Introductionmentioning

confidence: 99%

On the Fuzzy Solution of Linear-Nonlinear Partial Differential Equations

Osman

Xia²,

Omer³

et al. 2022

Mathematics

View full text Add to dashboard Cite

show abstract

“…In [8], the authors discussed an approximate scheme for solving one-dimensional heatlike and wave-like equations in fuzzy environments based on the homotopy perturbation method (HPM). In particular, the authors formulated the double parametric fuzzy HPM.…”

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confidence: 99%