Generalized Lucas polynomial sequence approach for fractional differential equations

Abstract

This article is interested in presenting and implementing two new numerical algorithms for solving multi-term fractional differential equations. The idea behind the proposed algorithms is based on establishing a novel operational matrix of fractional-order differentiation of generalized Lucas polynomials in the Caputo sense. This operational matrix serves as a powerful tool for obtaining the desired numerical solutions. The resulting solutions are spectral, and they are built on utilizing tau and collocation methods. A new treatment of convergence and error analysis of the suggested generalized Lucas expansion is presented. The presented numerical results demonstrate the efficiency, applicability and high accuracy of the proposed algorithms.