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

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.

Numerical Solution of Generalized Delay Integro-Differential Equations via Galerkin-Vieta-Lucas Polynomials

“…The inner product of V ) and other properties are given in (Issa et al, 2024); (Agarwal and El-Sayed, 2020); (Youssef et. al., 2022).…”

The analysis of a novel COVID-19 model with the fractional-order incorporating the impact of the vaccination campaign in Nigeria via the Laplace-Adomian Decomposition Method

“…For example in Refs. [42,43], the authors utilize compact finite differences and shifted Gegenbauer polynomials for discretizing time derivatives in space fractional order diffusion equations. They extend to shifted Vieta-Lucas polynomials, addressing generalized-fractional integro-differential equations with nonlocal boundary conditions through the Galerkin method.…”