In this paper, an efficient algorithm is proposed for solving one dimensional time-space-fractional
telegraph equations. The fractional derivatives are described in the conformable sense. This algorithm is
based on shifted Chebyshev polynomials of the fourth kind. The time-space fractional telegraph equations
is reduced to a linear system of second order differential equations and the Newmark’s method is applied
to solve this system. Finally, some numerical examples are presented to confirm the reliability and effectiveness
of this algorithm.