Numerical analysis of a two-parameter fractional telegraph equation

作者：Ford Neville J^*; Manuela Rodrigues M; Xiao Jingyu; Yan Yubin

来源：Journal of Computational and Applied Mathematics, 2013, 249: 95-106.

DOI：10.1016/j.cam.2013.02.009

• Fractional partial differential equation
• Fractional telegraph equation
• Finite difference method
• Stability
• Mittag-Leffler function

In this paper we consider the two-parameter fractional telegraph equation of the form %26lt;br%26gt;-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. %26lt;br%26gt;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 %26lt;= to to xo alpha %26lt; 1 and 0 %26lt;= beta %26lt; 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.

• 出版日期2013-9