TWO-DIMENSIONAL FRACTIONAL WAVE EQUATION VIA A NEW NUMERICAL APPROACH

The main goal of this work is to solve the fractional wave equation in two dimensions numerically with the use of some novel fractional formulas. In particular, the proposed approach used to deal with the fractional wave equation introduces two novel fractional difference formulas for approximating the Caputo differentiator of order δ and 2δ, respectively, where 0 < δ ≤ 1. Such formulas, which are derived based on the Lagrange interpolating polynomial, can generate a system of linear equations that can be solved numerically to obtain, ultimately, good approximate solutions to the fractional wave equation for different fractional-order values.