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 equationshaving multiple space and time delays by proposing a novel matrix-collocation methoddependent on the Delannoy polynomial. This method enables easy and fast approximationtool consisting of the matrix expansions of the functions using only the Delannoypolynomial. Thus, the solutions are obtained directly from a unique matrix system. Also, theresidual error computation, which involves the same procedure as the method, provides theimprovement of the solutions. The method is evaluated under some valuable error tests in thenumerical applications. To do this, a unique computer module is devised. The present resultsare compared with those of the existing methods in the literature, in order to oversee theprecision and efficiency of the method. One can express that the proposed method admitsvery consistent approximation for the equations in question.