A hybrid technique based on Lucas polynomials for solving fractional diffusion partial differential equation

Abstract

This paper presents a new numerical technique to approximate solutions of diffusion partial differential equations with Caputo fractional derivatives. We use a spectral collocation method based on Lucas polynomials for time fractional derivatives and a finite difference scheme in space. Stability and error analyses of the proposed technique are established. To demonstrate the reliability and efficiency of our new technique, we applied the method to a number of examples. The new technique is simply applicable, and the results show high efficiency in calculation and approximation precision.