Approximate analytical solution of fractional-order generalized integro-differential equations via fractional derivative of shifted Vieta-Lucas polynomial

Authors

  • Kazeem Issa Department of Mathematics and Statistics, Kwara State University, Malete, Kwara State, P. M. B. 1530, Ilorin Nigeria.
  • Risikat A. Bello Department of Mathematics and Statistics, Kwara State University, Malete, Kwara State, P. M. B. 1530, Ilorin Nigeria.
  • Usman Jos Abubakar Department of Mathematics, University of Ilorin, P. M. B. 1515, Ilorin Nigeria. https://orcid.org/0000-0002-2079-5731

Keywords:

Vieta-Lucas polynomial, Caputo fractional derivative, Generalized-fractional integro-differential equation, Galerkin method

Abstract

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.

Dimensions

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Published

2024-03-06

How to Cite

Approximate analytical solution of fractional-order generalized integro-differential equations via fractional derivative of shifted Vieta-Lucas polynomial. (2024). Journal of the Nigerian Society of Physical Sciences, 6(1), 1821. https://doi.org/10.46481/jnsps.2024.1821

Issue

Volume 6, Issue 1, February 2024

Section

Mathematics & Statistics
Copyright & Licensing

Copyright (c) 2024 Kazeem Issa, Risikat A. Bello, Usman Jos Abubakar

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

How to Cite

Approximate analytical solution of fractional-order generalized integro-differential equations via fractional derivative of shifted Vieta-Lucas polynomial. (2024). Journal of the Nigerian Society of Physical Sciences, 6(1), 1821. https://doi.org/10.46481/jnsps.2024.1821