A matrix method based on Lucas Polynomials for solving Fractional Differential Equation

Abstract

Our work is categories into two sections. First section concerns with originatingan operational matrix for fractional derivative of Lucas polynomials. With the help of this matrix,a spectral algorithm for solving some fractional-order initial value problems is exhibited and implemented. And the second section deal with a matrix whose entries are the coefficients appearing in the expansion of the derivative of Fibonacci polynomials and whose the sum of the elements in the same row gives the first order derivative of classical Fibonacci sequence at