No abstract

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.

In this paper of the series, the initial value problem for parabolic motion is considered analytically and computationally. A Mathematica program for this problem is established together with the powerful modified top-down continued fraction evaluation algorithm for the ratio of two hypergeometric functions. Numerical applications of the program are also included.