A matrix method based on the Fibonacci polynomials for solving fractional differential equations

This paper is concerned with deriving an operational matrix of fractional-order derivative of Fibonacci polynomials. As an application of this matrix, a spectral algorithm for solving some fractional-order initial value problems is exhibited and implemented. The properties of Fibonacci polynomials are presented. The operational matrix of derivative and productare given. This matrix is then utilized to reduce the solution of the fractional differential equations (FDEs) to a system of algebraic equations. Illusrative examples are included to demonstrate the validity and applicability of the technique.