Analytical Solution of Generalized Fractional Integro-Di erential Equations via Shifted Gegenbauer Polynomials
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Date
2024-12-31
Authors
Kazeem Issa
Adebayo Ridwan
Muritala Hambali Sulaiman
Journal Title
Journal ISSN
Volume Title
Publisher
MATEMATIKA, MJIAM, Volume 40, Number 3, 113{129 c Penerbit UTM Press. All rights reserved
Abstract
Abstract In this paper, we proposed an analytical solution for generalized fractional order integro-di erential equations with non-local boundary conditions via shifted Gegenbauer polynomials as an approximating polynomial using the Galerkin method and collocation techniques involving operational matrix that make use of the Liouville-Caputo operator of differentiation in combination with Gegenbauer polynomials. Shifted Gegenbauer polynomial properties were exploited to transform fractional order integro-differential equation and its non-local boundary conditions into an algebraic system of equations. Shifted Gegenbauer polynomial C_m^((α) ) (x) was used in order to generate and generalize the results of some other orthogonal polynomials by varying the value of parameter . The accuracy and effctiveness of the proposed method are tested on some selected examples from the literature. We observed that, when the exact solution is in polynomial form, the approximate solution gives a closed form solution, and non-polynomial exact solution, also give better results compared to the existing results in the literature.