Fractional Bell collocation method for solving linear fractional integro-differential equations

YÜZBAŞI Ş.

Mathematical Sciences, cilt.18, sa.1, ss.29-40, 2024 (SCI-Expanded) identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 18 Sayı: 1
  • Basım Tarihi: 2024
  • Doi Numarası: 10.1007/s40096-022-00482-0
  • Dergi Adı: Mathematical Sciences
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.29-40
  • Anahtar Kelimeler: 11B73, 34A08, 34K37, 65L60, Bell polynomials, Caputo fractional derivatives, collocation method, Fractional integro-differential equations
  • Akdeniz Üniversitesi Adresli: Evet

Özet

© 2022, The Author(s), under exclusive licence to Islamic Azad University.In this study, a collocation method based on the Bell poynomials is introduced for solving linear fractional integro-differential equations. Our aim in this study is to obtain the approximate solution of linear fractional integro-differential equations in the truncated fractional Bell series. Firstly, the fractional Bell functions which are a generalization of the Bell polynomials are expressed in matrix forms. Second, by Caputo derivative, the derivatives of the solution form are created for derivatives in the problem. By using the equal spacing points, we reduce the linear fractional problem to a system of linear algebraic equations. The gained this system is solved and its solutions give the coefficients of fractional Bell series which is the assumed solution. Lastly, error estimation is made and the method is applied to numerical examples.