| Citation: |
Ahlem BenRabah, Omar Abu Arqub. AN EFFECTIVE SUSTAINABLE COLLOCATION METHOD FOR SOLVING REGULAR/SINGULAR SYSTEMS OF CONFORMABLE DIFFERENTIAL EQUATIONS SUBJECT TO INITIAL CONSTRAINT CONDITIONS[J]. Journal of Applied Analysis & Computation, 2023, 13(3): 1336-1358. doi: 10.11948/20220138
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AN EFFECTIVE SUSTAINABLE COLLOCATION METHOD FOR SOLVING REGULAR/SINGULAR SYSTEMS OF CONFORMABLE DIFFERENTIAL EQUATIONS SUBJECT TO INITIAL CONSTRAINT CONDITIONS
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Abstract
The main objective of the present article is to provide an overview of the B-splines collocation methods (BSCM) to achieve practical analytical-numerical solutions for a family of regular/singular systems of initial constraints condition (ICC). Herein, the fractional derivatives are described by the conformable one, and an abundance of its basic theory is utilized. The useful properties of the cubic B-splines and collocation methods are employed to reduce the computations of both regular/singular systems of fractional order to a combination of linear/nonlinear algebraic equations. Numerical tests are treated quantitatively to demonstrate the technical statements and to exhibit the ability, perfection, and applicability of the suggested procedure for solving such conformable systems models. The outcomes confirm the reliability and efficacy of the technique improved. At the end of the manuscript, some notes were presented with some characteristics of the scheme and some possible future work.
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References
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Ahlem BenRabah, Omar Abu Arqub. AN EFFECTIVE SUSTAINABLE COLLOCATION METHOD FOR SOLVING REGULAR/SINGULAR SYSTEMS OF CONFORMABLE DIFFERENTIAL EQUATIONS SUBJECT TO INITIAL CONSTRAINT CONDITIONS[J]. Journal of Applied Analysis & Computation, 2023, 13(3): 1336-1358. doi: 10.11948/20220138
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Figure 1.
Results in Problem 1 when
$ m\mathrm{=50} $ $ \psi \left({\rho }_t\right) $ $ \widetilde{\psi }\left({\rho }_t\right) $ -
Figure 2.
Results in Problem 1 when
$ m\mathrm{=40} $ $ E_{\psi }\left({\rho }_t\right) $ $ E_{\phi }\left({\rho }_t\right) $ -
Figure 3.
Results in Problem 3: (a)
$ E_{\psi }\left({\rho }_t\right) $ $ m\mathrm{=100} $ $ E_{\phi }\left({\rho }_t\right) $ $ m\mathrm{=100} $ $ E_{\psi }\left({\rho }_t\right) $ $ m\mathrm{=200} $ $ E_{\phi }\left({\rho }_t\right) $ $ m\mathrm{=200} $ -
Figure 4.
Results in Problem 4 when
$ m\mathrm{=20} $ $ \psi \left({\rho }_t\right) $ $ \widetilde{\psi }\left({\rho }_t\right) $