A new approach based on the Zernike radial polynomials for numerical solution of the fractional diffusion-wave and fractional Klein-Gordon equations

摘要

This study aims to present some new numerical approximation schemes based on operational matrices of the Zernike radial polynomials (ZRPs), which are employed in solving fractional diffusion waves and fractional Klein-Gorden equations in fluid mechanics. First, some definitions of fractional calculus are given along some of the ZRPs and their operational matrices of derivative and fractional Riemann-Liouville integration. The main advantage of this approach is the reduction of the fractional diffusion-wave and fractional Klein-Gordon equation to the algebraic equations systems that can be solved easily, thus simplifying the problem. An estimation of the error is given. Finally, illustrative instances are discussed to shed more light on the validity and applicability of the presented method.