| Citation: |
Ali Akgül, Dumitru Baleanu, Enver Ülgül, Necibullah Sakar, Nourhane Attia. ANALYSIS OF NEW TRANSFER FUNCTIONS WITH SUM INTEGRAL TRANSFORMATION[J]. Journal of Applied Analysis & Computation, 2024, 14(6): 3282-3305. doi: 10.11948/20240001
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ANALYSIS OF NEW TRANSFER FUNCTIONS WITH SUM INTEGRAL TRANSFORMATION
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Abstract
We explore the novel SUM integral transform method for solving ordinary and partial differential equations, offering an effective approach beyond conventional Laplace and Sumudu transforms. Using this method, we address various differential equations, deriving transfer functions for classical and fractional derivatives. The resultant transfer functions provide valuable insights into diverse mathematical models.
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References
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Ali Akgül, Dumitru Baleanu, Enver Ülgül, Necibullah Sakar, Nourhane Attia. ANALYSIS OF NEW TRANSFER FUNCTIONS WITH SUM INTEGRAL TRANSFORMATION[J]. Journal of Applied Analysis & Computation, 2024, 14(6): 3282-3305. doi: 10.11948/20240001
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Figure 1.
SUM integral transform with the classical derivative
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Figure 2.
SUM integral transform with the Caputo derivative
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Figure 3.
SUM integral transform with the Modified Caputo-Fabrizio derivative
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Figure 4.
SUM integral transform with the Modified Atangana-Baleanu derivative
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Figure 5.
SUM integral transform with the Constant Proportional Caputo derivative
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Figure 6.
Transfer function for
$ a=e $ -
Figure 7.
Transfer function for
$ \phi=0.5, a=e $ -
Figure 8.
Transfer function (4.4) for
$ \phi=1 $ $ a=e $ -
Figure 9.
Transfer function (4.5) for
$ a=e, f(0)=1, $ $ \phi=\frac{1}{2} $ -
Figure 10.
Transfer function for
$ a=e, f(0)=1, \phi=\frac{1}{2}, k_1(\phi)=1, k_0(\phi)=1 $ -
Figure 11.
Transfer function for
$ a=e, c=3, R=2 $ -
Figure 12.
Transfer function for
$ a=e, C=2, R=1, L=1 $ -
Figure 13.
Transfer function (5.8) for
$ a=e, C=2, R=2, $ $ \phi=1 $ -
Figure 14.
Transfer function (5.9) for
$ C=1, a=e, R=3, $ $ \phi=1 $ -
Figure 15.
Transfer function (5.10) for
$ C=4, a=e, R=3, $ $ \phi=1 $ -
Figure 16.
Transfer function for
$ C=4, a=e, R=3, \phi=2, k_1(\phi)=1, k_0(\phi)=1 $ -
Figure 17.
Transfer function for
$ C=3, a=e, R=2, \phi=3, k_1(\phi)=1, k_0(\phi)=1 $ -
Figure 18.
Transfer function for
$ C=3, a=e, R=2, \phi=2, k_1(\phi)=1, k_0(\phi)=1 $