| Citation: |
Azzh Saad Alshehry, Saima Noor, Abdulkafi Mohammed Saeed, Ahmad Shafee, Rasool Shah. INNOVATIVE SOLUTIONS FOR FRACTIONAL WHITHAM-BROER-KAUP MODEL USING TRANSFORM-BASED METHODS[J]. Journal of Applied Analysis & Computation, 2025, 15(6): 3805-3825. doi: 10.11948/20250039
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INNOVATIVE SOLUTIONS FOR FRACTIONAL WHITHAM-BROER-KAUP MODEL USING TRANSFORM-BASED METHODS
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Abstract
This study investigates the application of the Elzaki Residual Power Series Method (ERPSM) and the New Iteration Transform Method (NITM) for solving fractional-order Whitham-Broer-Kaup system. These nonlinear fractional differential equations are fundamental models for describing complex wave dynamics and fluid mechanics phenomena. Using the fractional derivative by the proposed methods provides robust and efficient approaches for deriving analytical solutions regarding power series and other functional forms. The convergence and reliability of the methods are thoroughly analyzed, highlighting their ability to handle the intricate dynamics of fractionalorder systems. Numerical simulations and illustrative examples validate the accuracy and effectiveness of ERPSM and NITM in solving fractional-order Whitham-Broer-Kaup system. The findings demonstrate the potential of these methods to address a wide range of problems in mathematical physics, fluid dynamics, and nonlinear wave theory, offering new insights into fractional-order modeling.
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References
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Azzh Saad Alshehry, Saima Noor, Abdulkafi Mohammed Saeed, Ahmad Shafee, Rasool Shah. INNOVATIVE SOLUTIONS FOR FRACTIONAL WHITHAM-BROER-KAUP MODEL USING TRANSFORM-BASED METHODS[J]. Journal of Applied Analysis & Computation, 2025, 15(6): 3805-3825. doi: 10.11948/20250039
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Figure 1.
In Figure 1, ERPSM solution for (a), (b), (c) and (d) shows that fractional order at
$ \delta=1 $ $ \delta=0.8 $ $ \delta=0.6 $ $ \delta=0.4 $ $ \tau=0.3 $ $ \varphi{(\vartheta,\tau)} $ -
Figure 2.
In Figure 2, Comparison between ERPSM solution and exact for 3D plot of
$ \varphi{(\vartheta,\tau)} $ $ \tau=0.3 $ $ \delta=1 $ $ \delta=0.8 $ $ \delta=0.6 $ $ \delta=0.4 $ -
Figure 3.
In Figure 3, ERPSM solution for (a), (b), (c) and (d) shows that fractional order at
$ \delta=1 $ $ \delta=0.8 $ $ \delta=0.6 $ $ \delta=0.4 $ $ \tau=0.3 $ $ \phi{(\vartheta,\tau)} $ -
Figure 4.
In Figure 4, comparison between ERPSM solution and exact for 3D plot of
$ \phi{(\vartheta,\tau)} $ $ \tau=0.3 $ $ \delta=1 $ $ \delta=0.8 $ $ \delta=0.6 $ $ \delta=0.4 $ -
Figure 5.
In Figure 5, NITM solution for (a), (b), (c) and (d) shows that fractional order at
$ \delta=1 $ $ \delta=0.8 $ $ \delta=0.6 $ $ \delta=0.4 $ $ \tau=0.3 $ $ \varphi{(\vartheta,\tau)} $ -
Figure 6.
In Figure 6, comparison between NITM solution and exact for 3D plot of
$ \varphi{(\vartheta,\tau)} $ $ \tau=0.3 $ $ \delta=1 $ $ \delta=0.8 $ $ \delta=0.6 $ $ \delta=0.4 $ -
Figure 7.
In Figure 7, NITM solution for (a), (b), (c) and (d) shows that fractional order at
$ \delta=1 $ $ \delta=0.8 $ $ \delta=0.6 $ $ \delta=0.4 $ $ \tau=0.3 $ $ \phi{(\vartheta,\tau)} $ -
Figure 8.
In Figure 8, comparison between NITM solution and exact for 3D plot of
$ \phi{(\vartheta,\tau)} $ $ \tau=0.3 $ $ \delta=1 $ $ \delta=0.8 $ $ \delta=0.6 $ $ \delta=0.4 $