Approximate solutions for solving nonlinear variable-order fractional riccati differential equations

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

Nonlinear Analysis: Modelling and Control, cilt.24, sa.2, ss.176-188, 2019 (SCI-Expanded) identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 24 Sayı: 2
  • Basım Tarihi: 2019
  • Doi Numarası: 10.15388/na.2019.2.2
  • Dergi Adı: Nonlinear Analysis: Modelling and Control
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.176-188
  • Anahtar Kelimeler: Fractional calculus, Fractional riccati differential equation, Riemann-liouville fractional derivative of variable order, Shifted chebyshev polynomials, Spectral collocation method
  • İstanbul Gelişim Üniversitesi Adresli: Hayır

Özet

In this manuscript, we introduce a spectral technique for approximating the variableorder fractional Riccati differential equation (VOFRDE). Firstly, the solution and its space fractional derivatives is expanded as shifted Chebyshev polynomials series. Then we determine the expansion coefficients by reducing the VOFRDEs and its conditions to a system of algebraic equations. We show the accuracy and applicability of our numerical approach through four numerical examples.