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- Title
A Novel Operational Matrix of Caputo Fractional Derivatives of Fibonacci Polynomials: Spectral Solutions of Fractional Differential Equations.
- Authors
Abd-Elhameed, Waleed M.; Youssri, Youssri H.
- Abstract
Herein, two numerical algorithms for solving some linear and nonlinear fractional-order differential equations are presented and analyzed. For this purpose, a novel operational matrix of fractional-order derivatives of Fibonacci polynomials was constructed and employed along with the application of the tau and collocation spectral methods. The convergence and error analysis of the suggested Fibonacci expansion were carefully investigated. Some numerical examples with comparisons are presented to ensure the efficiency, applicability and high accuracy of the proposed algorithms. Two accurate semi-analytic polynomial solutions for linear and nonlinear fractional differential equations are the result.
- Subjects
DIFFERENTIAL equations; FRACTIONAL calculus; BESSEL functions; VAN der Pol oscillators (Physics); POLYNOMIALS; SPECTRAL sequences (Mathematics); RAYLEIGH number
- Publication
Entropy, 2016, Vol 18, Issue 10, p345
- ISSN
1099-4300
- Publication type
Article
- DOI
10.3390/e18100345