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«THE BULLETIN OF IRKUTSK STATE UNIVERSITY». SERIES «MATHEMATICS»
«IZVESTIYA IRKUTSKOGO GOSUDARSTVENNOGO UNIVERSITETA». SERIYA «MATEMATIKA»
ISSN 1997-7670 (Print)
ISSN 2541-8785 (Online)

List of issues > Series «Mathematics». 2023. Vol 45

Numerical Solution of Fractional Order Fredholm Integro-differential Equations by Spectral Method with Fractional Basis Functions

Author(s)
Y. Talaei1, S. Noeiaghdam2,3, H. Hosseinzadeh4

1University of Mohaghegh Ardabili, Ardabil, Iran

2Irkutsk National Research Technical University, Irkutsk, Russian Federation

3South Ural State University, Chelyabinsk, Russian Federation

4Ardabil Branch, Islamic Azad University, Ardabil, Iran

Abstract
This paper introduces a new numerical technique based on the implicit spectral collocation method and the fractional Chelyshkov basis functions for solving the fractional Fredholm integro-differential equations. The framework of the proposed method is to reduce the problem into a nonlinear system of equations utilizing the spectral collocation method along with the fractional operational integration matrix. The obtained algebraic system is solved using Newton’s iterative method. Convergence analysis of the method is studied. The numerical examples show the efficiency of the method on the problems with non-smooth solutions.
About the Authors

Y. Talaei, Dr. Sci., (PhD), University of Mohaghegh Ardabili, Ardabil, Iran, ytalaei@gmail.com, y.talaei@yahoo.com

Samad Noeiaghdam, Dr. Sci. (PhD), Assoc. Prof., Irkutsk National Research Technical University, Irkutsk, 664074, Russian Federation; South Ural State University, Chelyabinsk, 454080, Russian Federation, noiagdams@susu.ru

H. Hosseinzadeh, Dr. Sci. (PhD), Assoc. Prof., Ardabil Branch, Islamic Azad University, Ardabil 5615883895, Iran. hasan hz2003@yahoo.com

For citation
Talaei Y., Noeiaghdam S., Hosseinzadeh H. Numerical Solution of Fractional Order Fredholm Integro-differential Equations by Spectral Method with Fractional Basis Functions. The Bulletin of Irkutsk State University. Series Mathematics, 2023, vol. 45, pp. 89–103. https://doi.org/10.26516/1997-7670.2023.45.89
Keywords
fractional integro-differential equations, fractional order Chelyshkov polynomials, spectral collocation method, convergence analysis
UDC
518.517
MSC
65N35, 47G20, 35R11, 42C10
DOI
https://doi.org/10.26516/1997-7670.2023.45.89
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