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, vol.24, no.2, pp.176-188, 2019 (SCI-Expanded) identifier

  • Publication Type: Article / Article
  • Volume: 24 Issue: 2
  • Publication Date: 2019
  • Doi Number: 10.15388/na.2019.2.2
  • Journal Name: Nonlinear Analysis: Modelling and Control
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.176-188
  • Keywords: Fractional calculus, Fractional riccati differential equation, Riemann-liouville fractional derivative of variable order, Shifted chebyshev polynomials, Spectral collocation method
  • Istanbul Gelisim University Affiliated: No

Abstract

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.