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

Bhrawy A. H., Abdelkawyy M. A., Baleanu D., AHMED ZAKI MAHAMED AMIN A. Z. M. A.

Hacettepe Journal of Mathematics and Statistics, vol.47, no.3, pp.553-566, 2018 (SCI-Expanded) identifier

  • Publication Type: Article / Article
  • Volume: 47 Issue: 3
  • Publication Date: 2018
  • Doi Number: 10.15672/hjms.2017.478
  • Journal Name: Hacettepe Journal of Mathematics and Statistics
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, TR DİZİN (ULAKBİM)
  • Page Numbers: pp.553-566
  • Keywords: Gauss quadrature, Shifted Chebyshev polynomial, Shifted Legendre polynomials, Spectral collocation method, Two-dimensional fractional integral equations with weakly singular
  • Istanbul Gelisim University Affiliated: Yes

Abstract

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.