Numerical Solution of Fractional Riccati Differential Equation via Shifted Chebyshev Polynomials of the Third Kind

Year 2017, Volume: 2 Issue: 1, 1 - 11, 30.04.2017

Handan Yaslan

https://doi.org/10.30931/jetas.304377

Cited By: 3

Abstract

In this paper, Chebyshev collocation method is applied to fractional Riccati differential equation (FRDE) using the shifted Chebyshev polynomials of the third kind. Approximate analytical solution of FRDE is considered as Chebyshev series expansion. The fractional derivative is described in the Caputo sense. Using properties of Chebyshev polynomials FRDE with initial condition is reduced to a nonlinear system of algebraic equations which solved by the Newton iteration method. The accuracy and efficiency of the proposed method is illustrated by numerical examples.

Keywords

Fractional Riccati differential equation, Shifted Chebyshev polynomials of the third kind, Chebyshev collocation method, Caputo fractional derivative

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