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An Observation on the Elzaki Transform and the Fractional Coupled System of PDEs Cover

An Observation on the Elzaki Transform and the Fractional Coupled System of PDEs

Acta Mechanica et Automatica
Volume 19 (2025): Issue 3 (September 2025)
By: Mohammed E. A. RABIE and  Tarig M. ELZAKI  
Open Access
|Sep 2025

Figures & Tables

Fig.1.

(a) Comparing the provided method's 3D representations of the solutions to the exact solutions for Eq. (8), the outcome in comparison to the exact solutions, (b) represent the solutions at κ = 0.95,0.9,0.85
(a) Comparing the provided method's 3D representations of the solutions to the exact solutions for Eq. (8), the outcome in comparison to the exact solutions, (b) represent the solutions at κ = 0.95,0.9,0.85

Fig. 2.

(a) Comparing the provided method's 3D representations of the solutions to the exact solutions for Eq. (11), P(υ, ζ, τ) the outcome in comparison to the exact solutions, (b) represent the solutions at κ = 0.95,0.9,0.85
(a) Comparing the provided method's 3D representations of the solutions to the exact solutions for Eq. (11), P(υ, ζ, τ) the outcome in comparison to the exact solutions, (b) represent the solutions at κ = 0.95,0.9,0.85

Fig. 3.

(a) Comparing the provided method's 3D representations of the solutions to the exact solutions for Eq. (11), Q(υ, ζ, τ) the outcome in comparison to the exact solutions, (b) represent the solutions at κ = 0.95,0.9,0.85
(a) Comparing the provided method's 3D representations of the solutions to the exact solutions for Eq. (11), Q(υ, ζ, τ) the outcome in comparison to the exact solutions, (b) represent the solutions at κ = 0.95,0.9,0.85

Fig.4.

(a) Comparing the provided method's 3D representations of the solutions to the exact solutions for Eq. (11), K(υ, ζ, τ) the outcome in comparison to the exact solutions, (b) represent the solutions at κ = 0.95,0.9,0.85
(a) Comparing the provided method's 3D representations of the solutions to the exact solutions for Eq. (11), K(υ, ζ, τ) the outcome in comparison to the exact solutions, (b) represent the solutions at κ = 0.95,0.9,0.85

j_ama-2025-0060_utab_001

Φ(τ)E [Φ(τ)] = T(o)
1o2
τo3
τnn! on+2
eaτo21−ao
sin a τao31+a2o2
cos a τo21+a2o2

The comparison of the exact and approximate solutions yields the numerical result for example (2)

ζτυκ = 0.85κ = 0.9κ = 0.95ExactError
01.082131.087121.091071.116280.0252107
π6 0.641040.6439950.6463320.6612660.0149344
K(υ, ζ, τ)0.10.01π3 0.3797420.3814930.3828770.3917240.00884693
π2 0.2249540.2259910.2268110.2320510.00524079

The comparison of the exact and approximate solutions yields the numerical result for example (1)

τυκ = 0.85κ = 0.9κ = 0.95ExactError
00.0.0.0.0.
π6 0.4895780.4918350.4936190.4950250.00140562
P(υ, τ)Q(υ, τ)0.01π3 0.8479730.8518830.8549740.8574080.00243461
π2 0.9791550.983670.9872390.990050.00281124
DOI: https://doi.org/10.2478/ama-2025-0060 | Journal eISSN: 2300-5319 | Journal ISSN: 1898-4088
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Language: English
Page range: 518 - 524
Submitted on: Feb 4, 2025
|
Accepted on: Jun 16, 2025
|
Published on: Sep 30, 2025
Published by: Bialystok University of Technology
In partnership with: Paradigm Publishing Services
Publication frequency: 4 issues per year
Keywords:
Fractional Coupled System of Nonlinear Partial Differential Equations,
Novel Analytical Method,
Elzaki Transform,
Mittag-Leffler
Related subjects:
Engineering,
Electrical engineering,
Electronics,
Mechanical engineering,
Mechanics,
Bioengineering and biomedical engineering,
Biomechanics,
Civil engineering,
Environmental engineering

© 2025 Mohammed E. A. RABIE, Tarig M. ELZAKI, published by Bialystok University of Technology
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

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