Approximate solutions for solving nonlinear variable-order fractional Riccati differential equations
Eid H. Doha
Cairo University
Mohamed A. Abdelkawy
Al-Imam Mohammad Ibn Saud Islamic University
Ahmed Z.M. Amin
Canadian International College
Dumitru Baleanu
Cankaya University
Published 2019-02-01


fractional calculus
Riemann–Liouville fractional derivative of variable order
fractional Riccati differential equation
spectral collocation method
shifted Chebyshev polynomials

How to Cite

Doha E. H., Abdelkawy M. A., Amin A. Z. and Baleanu D. (2019) “Approximate solutions for solving nonlinear variable-order fractional Riccati differential equations”, Nonlinear Analysis: Modelling and Control, 24(2), pp. 176–188. doi: 10.15388/NA.2019.2.2.


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


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