A discrete orthogonal polynomials approach for coupled systems of nonlinear fractional order integro-differential equations
L. Moradi, F. Mohammadi, D. Conte
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.
Tbilisi Mathematical Journal, Vol. 12(3) (2019), pp. 21-38