Numerical solutions of fractional system, two-point BVPs using iterative reproducing kernel algorithm
We propose an efficient computational method, namely, the iterative reproducing kernel method for the approximate solution of fractional-order systems of two-point time boundary-value problems in the Caputo sense. Two extended inner-product spaces are constructed in which the boundary conditions of...
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| Дата: | 2018 |
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| Автори: | , , , , , , , |
| Формат: | Стаття |
| Мова: | Англійська |
| Опубліковано: |
Institute of Mathematics, NAS of Ukraine
2018
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| Онлайн доступ: | https://umj.imath.kiev.ua/index.php/umj/article/view/1580 |
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| Назва журналу: | Ukrains’kyi Matematychnyi Zhurnal |
| Завантажити файл: |  |
Репозитарії
Ukrains’kyi Matematychnyi Zhurnal| Резюме: | We propose an efficient computational method, namely, the iterative reproducing kernel method for the approximate solution
of fractional-order systems of two-point time boundary-value problems in the Caputo sense. Two extended inner-product
spaces are constructed in which the boundary conditions of the systems are satisfied. The reproducing kernel functions
are constructed to get an accurate algorithm for the investigation of fractional systems. The developed procedure is based
on generating the orthonormal basis with an aim to formulate the solution throughout the evolution of the algorithm. The
analytic solution is represented in the form of a series in the reproducing kernel Hilbert space with readily computed
components. In this connection, some numerical examples are presented to show the good performance and applicability
of the developed algorithm. The numerical results indicate that the proposed algorithm is a powerful tool for the solution
of fractional models arising in different fields of sciences and engineering. |
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