Numerical solution method for multi-term variable order fractional differential equations by shifted Chebyshev polynomials of the third kind

TURAL POLAT S. N., TURAN DİNCEL A.

Alexandria Engineering Journal, cilt.61, sa.7, ss.5145-5153, 2022 (SCI-Expanded) identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 61 Sayı: 7
  • Basım Tarihi: 2022
  • Doi Numarası: 10.1016/j.aej.2021.10.036
  • 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.5145-5153
  • Anahtar Kelimeler: Multi-term fractional differential equations, Operational matrix method, Shifted Chebyshev polynomials of the third kind, Variable-order fractional differential equations
  • Yıldız Teknik Üniversitesi Adresli: Evet

Özet

Multi-term variable-order fractional differential equations (VO-FDEs) are considered to be one of the tools to illustrate the behavior of transient-regime real-life phenomena precisely. The analytical solutions of VO-FDEs are generally very hard to obtain. Therefore, in this study, an approximation method for the solution of multi-term VO-FDEs is proposed using shifted Chebyshev polynomials of the third kind (SCP3). The method employs the operational matrices of SCP3 to proximate the VO-FDEs with a system of algebraic equations. The solution of which also yields the approximate result for the multi-term VO-FDE. An error analysis is also included. The SCP3 method is examined on several examples demonstrating the precision and prowess of the method.