A spectral technique for solving two-dimensional fractional integral equations with weakly singular kernel

Yıl 2018, Cilt: 47 Sayı: 3, 553 - 566, 01.06.2018

Ali H. Bhrawy Mohamed A. Abdelkawy Dumitru Baleanu Ahmed Z.m. Amin

Öz

This paper adapts a new numerical technique for solving two-dimensional fractional integral equations with weakly singular. Using the spectral collocation method, the fractional operators of Legendre and Chebyshev polynomials, and Gauss-quadrature formula, we achieve a reduction of given problems into those of a system of algebraic equations. We apply the reported numerical method to solve several numerical examples in order to test the accuracy and validity. Thus, the novel algorithm is more responsible for solving two-dimensional fractional integral equations with weakly singular.

Anahtar Kelimeler

Two-dimensional fractional integral equations with weakly singular, Spectral collocation method, Gauss quadrature, Shifted Legendre polynomials, Shifted Chebyshev polynomial

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