Numerical solution of fractional delay differential equations via ‎Fibonnacci polynomials

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 fractional derivative is achieved. This matrix and collocation method
are utilized to reduce the solution of the fractional delay differential equations to a system of algebraic
equations which can be solved by using Newton's iterative method. Illustrative examples are included to
demonstrate the validity and applicability of the technique