Spectral technique for solving variable-order fractional Volterra integro-differential equations

Doha E., Abdelkawy M., Amin A. Z. M. A., Baleanu D.

Numerical Methods for Partial Differential Equations, cilt.34, sa.5, ss.1659-1677, 2018 (SCI-Expanded) identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 34 Sayı: 5
  • Basım Tarihi: 2018
  • Doi Numarası: 10.1002/num.22233
  • Dergi Adı: Numerical Methods for Partial Differential Equations
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.1659-1677
  • Anahtar Kelimeler: fractional calculus, Integro-differential equation, Riemann-Liouville fractional of variable order, shifted Legendre-Gauss-Lobatto quadrature, spectral collocation method
  • İstanbul Gelişim Üniversitesi Adresli: Hayır

Özet

This article, presented a shifted Legendre Gauss-Lobatto collocation (SL-GL-C) method which is introduced for solving variable-order fractional Volterra integro-differential equation (VO-FVIDEs) subject to initial or nonlocal conditions. Based on shifted Legendre Gauss-Lobatto (SL-GL) quadrature, we treat with integral term in the aforementioned problems. Via the current approach, we convert such problem into a system of algebraic equations. After that we obtain the spectral solution directly for the proposed problem. The high accuracy of the method was proved by several illustrative examples.