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