Addition Theorems Associated with the Generalized Mittag-Leffler Function

Using two physical problems involving the so-called fractional telegraph equation, two new addition theorems associated with the generalized Mittag-Leffler function are shown. As a by-product new sum rules associated with the two parameters Mittag-Leffler function and with the classical confluent hypergeometric function, which is the most general function involving two parameters, are also shown.