| Citation: |
Nazek A. Obeidat, Mahmoud S. Rawashdeh, Malak Q. Al Erjani. A NEW EFFICIENT TRANSFORM MECHANISM WITH CONVERGENCE ANALYSIS OF THE SPACE-FRACTIONAL TELEGRAPH EQUATIONS[J]. Journal of Applied Analysis & Computation, 2024, 14(5): 3007-3032. doi: 10.11948/20240037
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A NEW EFFICIENT TRANSFORM MECHANISM WITH CONVERGENCE ANALYSIS OF THE SPACE-FRACTIONAL TELEGRAPH EQUATIONS
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Abstract
This article's goal is to investigate the space-fractional telegraph equation using an effective method called the Adomian natural decomposition method (ANDM), which is a combination of the Adomian decomposition method (ADM) and the natural transform method (NTM). Using the Banach fixed point theorem, we explore proofs for the existence and uniqueness theorems applying it to a nonlinear differential equation. Using our method, exact solutions of the space-fractional telegraph equation and time-fractional diffusion problems have been obtained. To demonstrate the effectiveness of the suggested scheme, four examples are provided.
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References
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Nazek A. Obeidat, Mahmoud S. Rawashdeh, Malak Q. Al Erjani. A NEW EFFICIENT TRANSFORM MECHANISM WITH CONVERGENCE ANALYSIS OF THE SPACE-FRACTIONAL TELEGRAPH EQUATIONS[J]. Journal of Applied Analysis & Computation, 2024, 14(5): 3007-3032. doi: 10.11948/20240037
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Figure 1.
Exact solution to
$ \chi(s,z) $ $ \alpha=2 $ $ \alpha=1.2 $ -
Figure 2.
Exact solution to
$ \chi(s,z) $ $ \alpha=1.4 $ $ \alpha=1.6 $ -
Figure 3.
Exact solution to
$ \chi(s,z) $ $ \alpha=1.2, 1.4, 1.6, 1.8, 2 $ $ z=2 $ $ z=4 $ -
Figure 4.
Exact solution to
$ \chi(s,z) $ $ \alpha=2 $ $ \alpha=1.2 $ -
Figure 5.
Exact solution to
$ \chi(s,z) $ $ \alpha=1.4 $ $ \alpha=1.6 $ -
Figure 6.
Exact solution to
$ \chi(s,z) $ $ \alpha=1.2, 1.4, 1.6, 1.8, 2 $ $ z=2 $ $ z=3 $ -
Figure 7.
Exact solution to
$ \chi(s,z) $ $ \alpha=2 $ $ \alpha=1.2 $ -
Figure 8.
Exact solution to
$ \chi(s,z) $ $ \alpha=1.4 $ $ \alpha=1.6 $ -
Figure 9.
Exact solution to
$ \chi(s,z) $ $ \alpha=0.2, 0.4, 0.6, 0.8, 1 $ $ z=0.3 $ $ z=0.5 $ -
Figure 10.
Exact solution to
$ \chi(s,z) $ $ \alpha=2 $ $ \alpha=1.2 $ $ k=1 $ -
Figure 11.
Exact solution to
$ \chi(s,z) $ $ \alpha=1.4 $ $ \alpha=1.6 $ $ k=1 $ -
Figure 12.
Exact solution to
$ \chi(s,z) $ $ \alpha=1.2, 1.4, 1.6, 1.8, 2 $ $ z=0.5 $ $ z=1 $ $ k=1 $