| Citation: |
D. D. Pawar, R. D. Kadam, Sultan S Alshamrani, Wagdi F. S. Ahmed. EXPLORING THE DOUBLE ARA-KAMAL TRANSFORM FOR SOLVING FRACTIONAL PARTIAL DIFFERENTIAL EQUATIONS[J]. Journal of Applied Analysis & Computation, 2026, 16(3): 1226-1243. doi: 10.11948/20250038
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EXPLORING THE DOUBLE ARA-KAMAL TRANSFORM FOR SOLVING FRACTIONAL PARTIAL DIFFERENTIAL EQUATIONS
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Abstract
In this article, we explore the application of the double ARA-Kamal transformation (DARA-KT) to the nonlocal fractional Caputo derivative operator. Our investigation yields intriguing findings, particularly in solving certain classes of fractional partial differential equations (FPDEs). We delve into various physical scenarios, including Wave, Klein-Gordon, and Fokker-Planck equations, analyzing their implications. The incorporation of the DARA-KT technique proves to be both efficient and precise in deriving exact solutions for FPDEs. To demonstrate the practicality of our approach, we present some numerical examples and figures.
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References
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Math., 2021, 14, 2150029. doi: 10.1142/S1793557121500297 -
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D. D. Pawar, R. D. Kadam, Sultan S Alshamrani, Wagdi F. S. Ahmed. EXPLORING THE DOUBLE ARA-KAMAL TRANSFORM FOR SOLVING FRACTIONAL PARTIAL DIFFERENTIAL EQUATIONS[J]. Journal of Applied Analysis & Computation, 2026, 16(3): 1226-1243. doi: 10.11948/20250038
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Figure 1.
A) The plots display the exact solution for
$ \zeta = 1 $ $ \zeta = 0.95 $ $ \zeta = 0.85 $ $ \zeta = 0.75 $ $ \zeta $ $ f(x, t) $ $ \zeta = 1 $ -
Figure 2.
A) Plots show the exact solution for
$ \zeta = 1 $ $ \zeta = 0.95 $ $ 0.85 $ $ 0.75 $ $ \zeta $ $ f(x, t) $ $ \zeta = 1 $ -
Figure 3.
A) plot shows how the exact solution behaves when ζ = 2, compared to how it changes for different values of ζ = 1.95, 1.85, and 1.75. Each line represents the solution for one of these values of ζ, illustrating how the solution shifts as ζ decreases from 2. B) The surface graph of the solution f(x, t) for the Klein-Gordon equation at ζ = 1 for the problem in Example 5.3.
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Figure 4.
A) The plot shows the exact solution of when ζ = 1 and compares it to the solutions for different values of
$ \zeta = 0.95 $ $ 0.85 $ $ 0.75 $