Approximate analytical solution of fractional-order generalized integro-differential equations via fractional derivative of shifted Vieta-Lucas polynomial
In this paper, we extend fractional-order derivative for the shifted Vieta-Lucas polynomial to generalized-fractional integro-differential equations involving non-local boundary conditions using Galerkin method as transformation technique and obtained N - \delta + 1 system of linear algebraic equat...
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| Format: | Article |
| Language: | English |
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Nigerian Society of Physical Sciences
2024-01-01
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| Series: | Journal of Nigerian Society of Physical Sciences |
| Subjects: | |
| Online Access: | https://journal.nsps.org.ng/index.php/jnsps/article/view/1821 |
| _version_ | 1797317252495704064 |
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| author | Kazeem Issa Risikat A. Bello Usman Jos Abubakar |
| author_facet | Kazeem Issa Risikat A. Bello Usman Jos Abubakar |
| author_sort | Kazeem Issa |
| collection | DOAJ |
| description |
In this paper, we extend fractional-order derivative for the shifted Vieta-Lucas polynomial to generalized-fractional integro-differential equations involving non-local boundary conditions using Galerkin method as transformation technique and obtained N - \delta + 1 system of linear algebraic equations with \lambda i, i = 0, . . . , N unknowns, together with \delta non-local boundary conditions, we obtained (N + 1)- linear equations. The accuracy and effectiveness of the scheme was tested on some selected problems from the literature. Judging from the table of results and figures, we observed that the approximate solution corresponding to the problem that has exact solution in polynomial form gives a closed form solution while problem with non-polynomial exact solution gives better accuracy compared to the existing results.
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| first_indexed | 2024-03-08T03:32:14Z |
| format | Article |
| id | doaj.art-5dfff64e7b0a40fea661e2b8c02f46dc |
| institution | Directory Open Access Journal |
| issn | 2714-2817 2714-4704 |
| language | English |
| last_indexed | 2024-03-08T03:32:14Z |
| publishDate | 2024-01-01 |
| publisher | Nigerian Society of Physical Sciences |
| record_format | Article |
| series | Journal of Nigerian Society of Physical Sciences |
| spelling | doaj.art-5dfff64e7b0a40fea661e2b8c02f46dc2024-02-10T16:27:48ZengNigerian Society of Physical SciencesJournal of Nigerian Society of Physical Sciences2714-28172714-47042024-01-016110.46481/jnsps.2024.1821Approximate analytical solution of fractional-order generalized integro-differential equations via fractional derivative of shifted Vieta-Lucas polynomialKazeem Issa0Risikat A. Bello1Usman Jos Abubakar2https://orcid.org/0000-0002-2079-5731Department of Mathematics and Statistics, Kwara State University, Malete, Kwara State, P. M. B. 1530, Ilorin Nigeria.Department of Mathematics and Statistics, Kwara State University, Malete, Kwara State, P. M. B. 1530, Ilorin Nigeria.Department of Mathematics, University of Ilorin, P. M. B. 1515, Ilorin Nigeria. In this paper, we extend fractional-order derivative for the shifted Vieta-Lucas polynomial to generalized-fractional integro-differential equations involving non-local boundary conditions using Galerkin method as transformation technique and obtained N - \delta + 1 system of linear algebraic equations with \lambda i, i = 0, . . . , N unknowns, together with \delta non-local boundary conditions, we obtained (N + 1)- linear equations. The accuracy and effectiveness of the scheme was tested on some selected problems from the literature. Judging from the table of results and figures, we observed that the approximate solution corresponding to the problem that has exact solution in polynomial form gives a closed form solution while problem with non-polynomial exact solution gives better accuracy compared to the existing results. https://journal.nsps.org.ng/index.php/jnsps/article/view/1821Vieta-Lucas polynomialCaputo fractional derivativeGeneralized-fractional integro-differential equationGalerkin method |
| spellingShingle | Kazeem Issa Risikat A. Bello Usman Jos Abubakar Approximate analytical solution of fractional-order generalized integro-differential equations via fractional derivative of shifted Vieta-Lucas polynomial Journal of Nigerian Society of Physical Sciences Vieta-Lucas polynomial Caputo fractional derivative Generalized-fractional integro-differential equation Galerkin method |
| title | Approximate analytical solution of fractional-order generalized integro-differential equations via fractional derivative of shifted Vieta-Lucas polynomial |
| title_full | Approximate analytical solution of fractional-order generalized integro-differential equations via fractional derivative of shifted Vieta-Lucas polynomial |
| title_fullStr | Approximate analytical solution of fractional-order generalized integro-differential equations via fractional derivative of shifted Vieta-Lucas polynomial |
| title_full_unstemmed | Approximate analytical solution of fractional-order generalized integro-differential equations via fractional derivative of shifted Vieta-Lucas polynomial |
| title_short | Approximate analytical solution of fractional-order generalized integro-differential equations via fractional derivative of shifted Vieta-Lucas polynomial |
| title_sort | approximate analytical solution of fractional order generalized integro differential equations via fractional derivative of shifted vieta lucas polynomial |
| topic | Vieta-Lucas polynomial Caputo fractional derivative Generalized-fractional integro-differential equation Galerkin method |
| url | https://journal.nsps.org.ng/index.php/jnsps/article/view/1821 |
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