This article is cited in 7 papers

Integro-differential equations and functional analysis

Numerical solution of fractional order Fredholm integro-differential equations by spectral method with fractional basis functions

Y. Talaei^a, S. Noeiaghdam^bc, H. Hosseinzadeh<sup>d

a</sup> University of Mohaghegh Ardabili, Ardabil, Iran
^b Irkutsk National Research Technical University, Irkutsk, Russian Federation
^c South Ural State University, Chelyabinsk, Russian Federation
^d Ardabil 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.

Keywords: fractional integro-differential equations, fractional order Chelyshkov polynomials, spectral collocation method, convergence analysis.

UDC: 518.517

MSC: 65N35, 47G20, 35R11, 42C10

Received: 14.02.2023
Revised: 21.04.2023
Accepted: 10.05.2023

Language: English

DOI: 10.26516/1997-7670.2023.45.89