Numerical analysis of a two-parameter fractional telegraph equation

Abstract

In this paper we consider the two-parameter fractional telegraph equation of the form −CDα+1 t+ 0 u(t,x)+CDβ+1 x+ 0 u(t,x)−CDα t+ 0 u(t,x)−u(t,x)=0. Here CDα t+ 0 ,CDα+1 t+ 0 ,CDβ+1 x+ 0 are operators of the Caputo-type fractional derivative, where 0≤ α<1and0≤β<1. A numerical method is introduced to solve this fractional telegraph equation and stability conditions for the numerical method are obtained. Numerical examples are given in the final section of the paper.