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Haar wavelets method for solving class of coupled systems of linear fractional Fredholm integro-differential equations
In this paper, firstly, the “ Haar wavelet method ” is used to give approximate solutions for coupled systems of linear fractional Fredholm integro-differential equations. Moreover, we consider the fractional derivative to be described in the Caputo sense. The general idea of this technique is simpl...
Autores principales: | , , |
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Formato: | Online Artículo Texto |
Lenguaje: | English |
Publicado: |
Elsevier
2023
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Materias: | |
Acceso en línea: | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC10558993/ https://www.ncbi.nlm.nih.gov/pubmed/37810092 http://dx.doi.org/10.1016/j.heliyon.2023.e19717 |
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author | Darweesh, Amer Al-Khaled, Kamel Al-Yaqeen, Omar Abu |
author_facet | Darweesh, Amer Al-Khaled, Kamel Al-Yaqeen, Omar Abu |
author_sort | Darweesh, Amer |
collection | PubMed |
description | In this paper, firstly, the “ Haar wavelet method ” is used to give approximate solutions for coupled systems of linear fractional Fredholm integro-differential equations. Moreover, we consider the fractional derivative to be described in the Caputo sense. The general idea of this technique is simply based on reducing this kinds of coupled systems into systems of algebraic equations which are easily to deal with and solve. Also, Laplace transform operator is included to develop a sophisticated approach which we called “ Laplace Haar wavelet method ” as an adjustment to “ Haar wavelet method ” to reduce the error and computational time. We provide illustrative examples to confirm validity, efficiency, accuracy, and applicability of the proposed methods. |
format | Online Article Text |
id | pubmed-10558993 |
institution | National Center for Biotechnology Information |
language | English |
publishDate | 2023 |
publisher | Elsevier |
record_format | MEDLINE/PubMed |
spelling | pubmed-105589932023-10-08 Haar wavelets method for solving class of coupled systems of linear fractional Fredholm integro-differential equations Darweesh, Amer Al-Khaled, Kamel Al-Yaqeen, Omar Abu Heliyon Research Article In this paper, firstly, the “ Haar wavelet method ” is used to give approximate solutions for coupled systems of linear fractional Fredholm integro-differential equations. Moreover, we consider the fractional derivative to be described in the Caputo sense. The general idea of this technique is simply based on reducing this kinds of coupled systems into systems of algebraic equations which are easily to deal with and solve. Also, Laplace transform operator is included to develop a sophisticated approach which we called “ Laplace Haar wavelet method ” as an adjustment to “ Haar wavelet method ” to reduce the error and computational time. We provide illustrative examples to confirm validity, efficiency, accuracy, and applicability of the proposed methods. Elsevier 2023-09-09 /pmc/articles/PMC10558993/ /pubmed/37810092 http://dx.doi.org/10.1016/j.heliyon.2023.e19717 Text en © 2023 The Author(s) https://creativecommons.org/licenses/by-nc-nd/4.0/This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/). |
spellingShingle | Research Article Darweesh, Amer Al-Khaled, Kamel Al-Yaqeen, Omar Abu Haar wavelets method for solving class of coupled systems of linear fractional Fredholm integro-differential equations |
title | Haar wavelets method for solving class of coupled systems of linear fractional Fredholm integro-differential equations |
title_full | Haar wavelets method for solving class of coupled systems of linear fractional Fredholm integro-differential equations |
title_fullStr | Haar wavelets method for solving class of coupled systems of linear fractional Fredholm integro-differential equations |
title_full_unstemmed | Haar wavelets method for solving class of coupled systems of linear fractional Fredholm integro-differential equations |
title_short | Haar wavelets method for solving class of coupled systems of linear fractional Fredholm integro-differential equations |
title_sort | haar wavelets method for solving class of coupled systems of linear fractional fredholm integro-differential equations |
topic | Research Article |
url | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC10558993/ https://www.ncbi.nlm.nih.gov/pubmed/37810092 http://dx.doi.org/10.1016/j.heliyon.2023.e19717 |
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