An efficient numerical scheme for fractional model of telegraph equation

Abstract

The present attempt is to design a novel approach for the numerical solution of fractional telegraph equation. The novelty of the paper exist in solving the time fractional telegraph equation with differential quadrature method based on cubic B-spline (MHB-DQM) for the fractional parameter 1<γ<2. Telegraph equation is used in electric transmission line to find distance and time. The fractional derivative involved in the equation is discretized using Caputo derivative. On the other hand, the terms involving space derivatives are approximated by fusion of differential quadrature method with modified version of cubic B-spline. Here B-spline acts as a basis to compute the weighted coefficients of differential quadrature method. This phenomenon reduce the PDE to the system of equations, which then are solved using suitable numerical technique. A matrix based technique is used to ensure the stability of the proposed scheme. Feasibility and applicability of this algorithm is performed using test problems. Approximate solutions obtained by MHB-DQM is portrayed through graph and tables in an interactive way. These results show that solution converges for smaller values of time and at various values of fractional parameter.