Lucas polynomials semi-analytic solution for fractional multi-term initial value problems

Abstract

Herein, we use the generalized Lucas polynomials to find an approximate numerical solution for fractional initial value problems (FIVPs). The method depends on the operational matrices for fractional differentiation and integration of generalized Lucas polynomials in the Caputo sense. We obtain these solutions using tau and collocation methods. We apply these methods by transforming the FIVP into systems of algebraic equations. The convergence and error analyses are discussed in detail. The applicability and efficiency of the method are tested and verified through numerical examples.