A new operational matrix of fractional derivative based on the generalized Gegenbauer-Humbert polynomials to solve fractional differential equations

Alkhalissi J. H. S., Emiroglu İ., Bayram M., Secer A., Tasci F.

ALEXANDRIA ENGINEERING JOURNAL, cilt.60, sa.4, ss.3509-3519, 2021 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 60 Sayı: 4
  • Basım Tarihi: 2021
  • Doi Numarası: 10.1016/j.aej.2021.02.012
  • Dergi Adı: ALEXANDRIA ENGINEERING JOURNAL
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Compendex, INSPEC, Directory of Open Access Journals
  • Sayfa Sayıları: ss.3509-3519
  • Yıldız Teknik Üniversitesi Adresli: Evet

Özet

In this paper, a new type of wavelet method to solve fractional differential equations (linear or nonlinear) is proposed. The proposed method is based on the generalized Gegenbauer-Humbert polynomial. First, we derived the operational matrices for integer and fractional order derivatives. Then, using these operational matrices with the proposed method, we transformed the given problem into a system of algebraic equations. Then, some linear and nonlinear examples were considered and discussed to confirm the efficiency and accuracy of the proposed method. (C) 2021 THE AUTHORS. Published by Elsevier BV on behalf of Faculty of Engineering, Alexandria University. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/).