Numerical analysis of a two-parameter fractional telegraph equation

In this paper we consider the two-parameter fractional telegraph equation of the form −CDt0+α+1u(t,x)+CDx0+β+1u(t,x)−CDt0+αu(t,x)−u(t,x)=0. Here CDt0+α, CDt0+α+1, CDx0+β+1 are operators of the Caputo-type fractional derivative, where 0≤α<10≤α<1 and 0≤β<10≤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.