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, cilt.47, sa.3, ss.553-566, 2018 (SCI-Expanded, Scopus, TRDizin) identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 47 Sayı: 3
  • Basım Tarihi: 2018
  • Doi Numarası: 10.15672/hjms.2017.478
  • Dergi Adı: Hacettepe Journal of Mathematics and Statistics
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, TR DİZİN (ULAKBİM)
  • Sayfa Sayıları: ss.553-566
  • Anahtar Kelimeler: Gauss quadrature, Shifted Chebyshev polynomial, Shifted Legendre polynomials, Spectral collocation method, Two-dimensional fractional integral equations with weakly singular
  • İstanbul Gelişim Üniversitesi Adresli: Evet

Özet

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.