Numerical solution of mixed-type fractional functional differential equations using modified Lucas polynomials

Abstract

There is an increasing interest in the field of functional and fractional differential equations. The lack of closed-form analytical solutions motivates the development of numerical methods for solving mixed-type fractional-order functional differential equations (MFFDEs) with retarded and neutral terms. This paper studies the solution of MFFDEs by a collocation technique with modified Lucas polynomials. The proposed method uses operational matrices to obtain an approximate solution by means of a system of linear algebraic equations. The accuracy of the proposed algorithm is verified with three illustrative examples.