Numerical analysis of a two-parameter fractional telegraph equation

In this paper we consider the two-parameter fractional telegraph equation of the form -D-C(t0+)alpha+1 u(t, x) + D-C(t0+)beta+1 u(t, x) - D-C(t0+)alpha u(t, x) - u(t, x) = 0. Here D-C(t0+)alpha, D-C(t0+)alpha+1, D-C(t0+)beta+1 are operators of the Caputo-type fractional derivative, where 0 <= to to xo alpha < 1 and 0 <= beta < 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. 0 2013 Elsevier B.V. All rights reserved.