A novel numerical implementation for solving time fractional telegraph differential equations having multiple space and time delays via Delannoy polynomial

Abstract

This paper is concerned with solving numerically the time fractional telegraph equations having multiple space and time delays by proposing a novel matrix-collocation method dependent on the Delannoy polynomial. This method enables easy and fast approximation tool consisting of the matrix expansions of the functions using only the Delannoy polynomial. Thus, the solutions are obtained directly from a unique matrix system. Also, the residual error computation, which involves the same procedure as the method, provides the improvement of the solutions. The method is evaluated under some valuable error tests in the numerical applications. To do this, a unique computer module is devised. The present results are compared with those of the existing methods in the literature, in order to oversee the precision and efficiency of the method. One can express that the proposed method admits very consistent approximation for the equations in question.