Title

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

Authors

Issa, Kazeem; Bello, Risikat A.; Abubakar, Usman Jos

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 - ⌈δ⌉ 1 system of linear algebraic equations with λi, i = 0, . . ., N unknowns, together with ⌈δ⌉ 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.

Subjects

INTEGRO-differential equations; POLYNOMIALS; GALERKIN methods; NUMERICAL analysis; ALGEBRA

Publication

Journal of Nigerian Society of Physical Sciences, 2024, Vol 6, Issue 1, p1

ISSN

2714-2817

Publication type

Academic Journal

DOI

10.46481/jnsps.2024.1821