Tbilisi Mathematical Journal

A discrete orthogonal polynomials approach for coupled systems of nonlinear fractional order integro-differential equations

L. Moradi, F. Mohammadi, and D. Conte

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Abstract

This paper develops a numerical approach for solving coupled systems of nonlinear fractional order integro-differential equations(NFIDE). Shifted discrete Chebyshev polynomials (SDCPs) have been introduced and their attributes have been checked. Fractional operational matrices for the orthogonal polynomials are also acquired. A numerical algorithm supported by the discrete orthogonal polynomials and operational matrices are used to approximate solution of coupled systems of NFIDE. The operational matrices of fractional integration and product are applied for approximate the unknown functions directly. These approximations were put in the coupled systems of NFIDE. A comparison has been made between the absolute error of approximate solutions of SDCPs method with previous published. The gained numerical conclusions disclose that utilizing discrete Chebyshev polynomials are more efficient in comparison to the other methods.

Article information

Source
Tbilisi Math. J., Volume 12, Issue 3 (2019), 21-38.

Dates
Received: 9 August 2018
Accepted: 20 June 2019
First available in Project Euclid: 26 September 2019

Permanent link to this document
https://projecteuclid.org/euclid.tbilisi/1569463232

Digital Object Identifier
doi:10.32513/tbilisi/1569463232

Mathematical Reviews number (MathSciNet)
MR4012381

Zentralblatt MATH identifier
07172323

Subjects
Primary: 33C45: Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.) [See also 42C05 for general orthogonal polynomials and functions]
Secondary: 34A08: Fractional differential equations 34A34: Nonlinear equations and systems, general

Keywords
coupled systems of nonlinear fractional order integro-differential equations discrete Chebyshev polynomials operational matrix CPU time

Citation

Moradi, L.; Mohammadi, F.; Conte, D. A discrete orthogonal polynomials approach for coupled systems of nonlinear fractional order integro-differential equations. Tbilisi Math. J. 12 (2019), no. 3, 21--38. doi:10.32513/tbilisi/1569463232. https://projecteuclid.org/euclid.tbilisi/1569463232


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